I was under the impression that he had become a Democrat late in the game, as part of running for President as the candidate of the Democratic Party. However, it appears that this impression was incorrect.
At least according to the senate.gov directory. If you go to the Senators page, he is listed, as he has been forever, as “I-VT”. Furthermore, if you go to the bio search page, which allows searches by name and party, a search for Sanders / Senate / Democrat returns no results, and a search for Sanders / Senate / Independent returns St. Bernie. (As a side note, there have been a number of Sanders in Congress, starting with Senator Wilbur Fiske Sanders, in office from 1890-1893.)
Well, I found this to be interesting, at any rate. Either the Senate’s web page needs updating, or Senator Sanders has not formally switched his party affiliation.