West Ham have agreed a transfer fee with Liverpool over the permanent transfer of Andy Carroll.
West Ham have confirmed the free-transfer signing of Romanian full-back Razvan Rat on an initial one-year deal.
Stock's move to Turf Moor from Doncaster on a two-year deal reunites the 30-year-old with former Bournemouth team-mate Howe.
Stock is Howe's sixth summer signing and the Clarets chief told the club's official website: "Brian is a very good footballer who will suit how we play.
"He is someone we admired for a long time. He had a really good career at Doncaster and I thought he was impressive in the games he played against us over the past couple of years.
"Experience and leadership are two things we haven't got a great deal of and I certainly think he will add in those two areas."