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Except for those legati created by the lex Gabinia and similar laws, all legati were appointed by the Senate. The governor couldn't just appoint them by himself - although it appears that, in practice, he nominated who he wanted and the Senate confirmed it.
The wikipedia quote is wrong in the sense that a legatus pro praetore only held delegated imperium. I don't think this has been fully explored, but my understanding of the difference between a simple legatus and a legatus pro praetore was that the latter was put in charge of the army/province by the imperator, whereas the former was simply a subordinate commander of senatorial rank. In either case, the legatus is entirely the subordinate of the imperator - hence Catulus' argument, in his speech in Cassius Dio against the lex Gabinia, that the plebs should appoint multiple independent commanders rather than allow Pompeius to appoint his own legati, since an independent imperator will fight for his own glory whereas a legatus fights for another's (and hence will not fight as well). I think Caesar expresses the same idea somewhere.
So, to clarify your question: the Senate chose the legati, probably those nominated by the imperator. The imperator could delegate imperium pro praetore to a legatus, usually if he was commanding the province or a sizeable army in his own right, and that was the imperator's call, in the field. However, certain plebiscites (starting with the lex Gabinia) allowed the imperator to name a number of legati pro praetore at the start of the campaign, who would fight pretty much independently.
The best place to look into this is Brennan's book on the praetorship or, if you read German, Kunkel and Wittmann's book on Staatsordnung und Staatspraxis.