The 31-year-old has signed a two-and-a-half-year contract at The Hawthorns with a 12-month option.
West Ham were also interested in signing Fletcher, but a move to Upton Park broke down last weekend.
Albion failed in deadline day moves to sign West Ham striker Carlton Cole and Norwich defender Martin Olsson, but kept Brown Ideye and Graham Dorrans.
Fletcher made 342 appearances for United but started only five times for the club after Louis van Gaal took over as manager in the summer.
The Scot, who recovered from chronic bowel disease ulcerative colitis to resume his career in December 2013, had been at Old Trafford since he was a schoolboy and helped the Red Devils win the Premier League title five times.
But with his contract set to expire in the summer he was granted a free transfer to help him find a new club in this transfer window.
"This is a fantastic new challenge for me in my career," Fletcher told West Brom's website.
"I've spent my career at Manchester United and it's all I've ever known. But I felt it was the right time to move and I'm not sentimental about doing that."
Fletcher is the second player signed by West Brom head coach Tony Pulis following the £4.75m capture of winger Callum McManaman from Wigan.
The Scotland captain will wear the number 24 shirt for the Baggies.
Albion had hoped to sign Cole and Olsson on a busy deadline day, with Dorrans set to join Norwich and Ideye linked with a move to Qatari club Al Gharafa.
But Cole was called back to West Ham when they did not sign Tottenham's Emmanuel Adebayor, and Olsson failed to arrive for a medical on time.
Chairman Jeremy Peace said: "We did not get all the business done that we might have but we are thrilled to bring in a player and a character of Darren's calibre.
""We were disappointed for Carlton because he was also excited about joining us but for reasons which were beyond our control we could not complete the deal. The same can be said for the proposal involving Martin Olsson and Graham.
"But we have always maintained that January is a difficult time to do business and we are very happy with the deals we have done."
West Brom have signed Scotland midfielder Darren Fletcher on a free transfer from Manchester United.