Is the LDS observance of the Sabbath on Sunday based on revelation?

According to LDS.org, the observance of the Sabbath on Sunday is based on Acts 20:7

And upon the first day of the week, when the disciples came together to break bread, Paul preached into them. . .

so apparently the early disciples met on Sunday (at least that time they did)

https://www.lds.org/topics/sabbath?lang=eng

According to fairmormon.org:

Latter-day Saints do not base their worship practices on an analysis of early Christian history, or on the comments of scholars in Biblical commentaries, though these sources can confirm Church teachings. Rather, the Saints follow the guidance of a living prophet. However, it seems clear that the Latter-day Saint practice of observing the day of rest and worship on Sunday—like most of the Christian world—is consistent with the earliest Christian practice of which we have record.

See Brian's answer

Interestingly, however, the most important aspect of Sabbath worship for the LDS seems to be the worship, and not the day on which it is held. Most LDS worship occurs on Sunday. General Authorities, who must often travel on conference assignments on Sunday, fast and receive the sacrament weekly on Thursdays. Church branches in Israel worship on Saturday. Branches in Muslim countries, such as Egypt, meet on Friday, the Muslim holy day. Wrote one account of the Church in Israel:

Jerusalem is home to three major religions: Judaism, Christianity, and Islam. None of the three shares the same day of worship. Islam recognizes Friday as a holy day, Judaism celebrates the Sabbath on Saturday, while Christianity generally adheres to a Sunday day of worship. These differences posed significant challenges in the lives of the Saints living in the Holy Land, and David Galbraith posed questions regarding this matter to President Lee during the Prophet's visit to Jerusalem [in September 1972].

Following President Lee's visit, branch president David Galbraith wrote a letter to the First Presidency wherein he outlined four major concerns and formally recommended that the day of worship for Latter-day Saints in the Holy Land be changed. The four concerns were as follows: First, for the Jews, public transportation ceases on Saturday, stores and places of entertainment are closed, and in Jerusalem the streets are full of families going to and from their synagogues. Second, Sunday, on the other hand, is a normal working day. Those attending the universities have classes, many of the children have school, and, in fact, everyone except those in the diplomatic corps have other obligations on that day. Third, the members were scattered throughout the country, and the majority relied on public transportation. It would be impossible to hold late afternoon or evening services on Sunday. Fourth, the members of the Church had been holding their meetings on the Jewish Sabbath rather than Sunday for some time with at least the tacit approval of the mission.

Two months after President Harold B. Lee's visit to the Holy Land, he authorized President David Galbraith to conduct worship services in Israel on the Jewish Sabbath (Saturday). This authorization is dated November 20, 1972. This decision in Israel served as a precedent to include Friday observance as a day of worship in countries of primarily Islamic populations, such as Egypt and Jordan.

Note that this is not an official source, but I have no real reason to doubt that this event happened as reported.

To finish, it seems like there is no clear commandment in Doctrine and Covenants to hold the sunday as Sabbath, but we do hold the sunday as Sabbath because the prophets have taught us so - and it seems to be consistent with the NT, or in other words, that has been the prophets' understanding of the scriptures so far (see Brian's answer).