Reid the latest new face at promoted Burnley
Reid, a free agent after his contract at The Hawthorns came to an end, becomes the fifth close-season arrival for Sean Dyche's side as they gear up for a return to the top flight.
The 33-year-old has agreed a one-year deal and follows Michael Kightly, who had been at Burnley on loan, Matt Gilks, Marvin Sordell and Matt Taylor in signing on at Turf Moor.
Burnley gained promotion from the Championship last season and manager Dyche, an ex-colleague of Reid at Millwall, is delighted to have brought in a player boasting close to 200 Premier League appearances from his spells at Blackburn Rovers and West Brom.
"Steven is a very strong-minded professional and he has had years in the Premier League so he has that bit of experience and know-how," Dyche told Burnley's official website.
"I know him personally from his younger days at Millwall and he was a very solid pro then and he still is now, perhaps a more rounded version of what he was then.
"Along with Matty Taylor we want that experience in the building as well as the vibrancy in the team.
"Both of those players played in some really awkward games for West Brom and West Ham respectively and hopefully that experience can rub off on others."
Reid added: "I had on-off talks with Sean throughout the summer. Obviously it was a long hard season with West Brom last term and I'm delighted to get the deal done.
"There has been other interest over the summer because I was available on a free transfer but this just felt like the right move back in the Premier League."