If we include Texas and Hawaii we could also mention the Republic of Crimea. There are similar quibbles about the legitimacy of these annexations. Western governments and their corporate and state media scoffed at the overwhelming vote for accession, but subsequent polls sponsored by the Canadian, German and US governments found consistent results, see Do the Crimean people prefer to be with Russia than with Ukraine?.

I'm surprised no one has brought this up, although the concept itself was a bit odd to me.

https://en.wikipedia.org/wiki/Franco-British_Union

The 1956 Mollet proposal is the particular instance I'm thinking of, even if it was knocked back.

The Far Eastern Republic (though not widely internationally recognized) joined Soviet Russia in 1922, and was completely integrated into the country. The merger was voluntary as the government has been a puppet of Russia anyway, but I guess the people very definitely did not want to remain separated from Russia.

Even the creation of the Soviet Union itself qualifies - merger of Russia, the Transcaucasian SFSR, Ukraine and Belorussia has been voluntary in the sense that their ruling governments approved the union, and people were not against (re)integration with Russia that much, though they might have quibbles with the current government and ruling party.

Following the lines Peter Erwin's answer, I think the EU should also be considered.

Legally, a country that joins the EU gives up on many aspects of its sovereignty to the new EU entity which is in practice mostly led by Germany and the other big western nations.

For the identity dynamics, which is I what I believe is in the essence of this question, many small countries are exchanging their old nationality with a European one which is again mostly defined by the big western nations.

Ossetia the Russian Empire, Tuva joined the USSR.

In 1963 Singapore and the Federation of Malaya merged to form Malaysia. Singapore became independant again in 1965.

Source: History of Singapore (Wikipedia).

One possible example was the temporary Peru-Bolivian Confederation of the late 1830s.

Peru and Bolivia had been "one territory" during the colonial era, but became separate countries during the wars of independence. After a brief war between the two countries, Peru's General Gamarra and Bolivia's General Santa Cruz agreed that the two countries should be re-united. Peru was the larger (populationwise) and stronger of the two countries, so it was more eager for a union, or at least a Confederation, in the earlier days.

Then "Peru" subdivided into North and South Peru, leaving Bolivia the strongest of the three parties, and General Santa Cruz nominally the head of the whole "country". That was not so acceptable to the Peruvians, especially the North Peruvians. These people sided in a new war with neighboring Chile and Argentina against Bolivia and "South" Peru. General Gamarra reunited the two Perus and ousted General Santa Cruz from the newly reunited country with foreign help, so Bolivia went its separate way, and Santa Cruz went into exile

Sikkim

In 1975, the Prime Minister of Sikkim appealed to the Indian Parliament for Sikkim to become a state of India. In April of that year, the Indian Army took over the city of Gangtok and disarmed the Chogyal's palace guards. Thereafter, a referendum was held in which 97.5 per cent of voters supported abolishing the monarchy, effectively approving union with India. On 16 May 1975, Sikkim became the 22nd state of the Indian Union, and the monarchy was abolished.

Source: Sikkim (Wikipedia).

I think East Germany could be considered to fit your question. It was annexed voluntarily by West Germany in 1990. It was called unification but for all practical reasons it was an annexation.

As I was born in and live in Saarland, I also would like to add the history of our small "country": we were separated from Germany twice (1919 and 1947) and formed a more or less independent country with close economical connections to France. But in both occasions, "we" (our predecessors) essentially voted to re-join Germany (in end-1934 and in 1955).

I think that the joining of Tanganyika and The People's Republic of Zanzibar and Pemba would fit your criteria. They changed the new country's name to Tanzania.

It is interesting most people seem to only study/remember European history.

Panama joined Colombia in its early years after it declared independence from Spain. They formed New Granada. For a while Colombia and Venezuela were joined as well forming the Grand Colombia in which the great Simon de Bolivar was president.

How about the Dominican Republic inviting Spain to retake administration in 1861?

The Dominican Republic has a complicated history that involves 3 attempts to voluntarily join another country. They won independence from Spain in 1822 and immediately joined Haiti. Then they won independence from Haiti in 1844, but 17 years of misrule led to an economic mess that the last president thought Spain could bail them out of. The re-occupation didn't go so well either, and they reasserted independence in 1865.

The new administration still wanted to hand over power to a bigger country, and tried to get the United States to take over, but the measure failed in the US Senate. That was probably all for the best, since the idea doesn't seem to have had popular support in the DR. The Dominican Republic has remained independent ever since.

United Arab Republic = Egypt + Syria

The United Arab Republic (UAR) was a short-lived political union between Egypt and Syria, from 1958 to 1961.

The UAR membership in the United Nations replaced the memberships of both Egypt and Syria.

Attalus III Philometor, 133 BC, leaves his kingdom to Rome.

The Wikipedia article on Attalus III has very little more to add.

Was this voluntary? There was an uprising following the occupation by Rome, with support of the neighboring kingdoms. One neighbor, Mithridates V, was a Roman ally, though he may have been playing a double game; certainly his son was doing so during his long reign.

More detail is found in the History of Rome, Vol. IV, p. 317

THE HISTORY OF ROME FROM THE FIRST PUNIC WAR TO THE DEATH OF CONSTANTINE. By B.G. NIEBUHR, published 1844. pp. 317-318

During this time Attalus Philometor, of Pergamus, had died, and with him the dynasty of the princes of Pergamus had become extinct. The first princes of that family were clever men, and of a mild disposition, although much may be said against their policy, if we take humanity as our standard. But the last Attalus was a man of different character: his reign was tyrannical, and he himself was one of those contemptible miscreants whom we meet with occasionally in the history of the East, where a little natural perversity is easily carried to the highest pitch, as in the case of the gluttony of Sultan Ibrahim. In the East, men sometimes take a delight in what is most unnatural and disgusting, and thus become true incarnations of a base and satanic nature. Such a man was Attalus. The only art he occupied himself with, was that of preparing poisons; and what amused him most was, to get rid of those who were his nearest in kindred. He died without issue, and left his whole kingdom to the Romans, who certainly would not easily have recognised any one else as his successor; for they looked upon his kingdom as their own property, which they had a right to claim, just as a master had the right of succession to the estate of his slave or his freedman, who died without having made a will. The remarks of Florus, therefore on this affair are foolish. But there was a natural son of Eumenes, the predecessor of Attalus, called Aristonicus, who claimed the kingdom of Attalus as his lawful inheritance; as however, there was no one in the world who could give him assistance, it is inconceivable how he could have the madness to believe that he would be able to hold out against the Romans, and how it was possible for him to find any support among the people of Pergamus. And yet the war lasted much longer than had been anticipated. The effeminate inhabitants of the magnificent country of Lydia and Ionia carried on the war with great resolution; and besides them, Aristonicus had many Thracian mercenaries in his army. On the part of the Romans, the war was badly conducted, as their generals thought of nothing else but enriching themselves, and turning everything into money, instead of making the proper use of their victories: they were, in fact, glad when a powerful and wealthy town revolted, because it afforded them an opportunity for plunder. The war was at length brought to an end by M. Perperna and M.' Aquillius. Aristonicus was taken prisoner at Stratonicea, and adorned the triumph at Rome. The Romans thus acquired an extremely rich province. The end of this, as well as of the Servile war, belongs to a later date than the year 619, which is the year of the tribuneship of Tib. Sempronius Gracchus. The reduction of Sicily falls in the year 620, and the defeat of Aristonicus in 622.