The 27-year-old former Bristol Rovers playmaker, who made 47 appearances for the Owls in their npower League One promotion-winning campaign last season, will link up with his new team-mates on Wednesday.
"Chris is a player I have admired for a number of years now; in fact he is a player I tried to sign two years ago," manager Karl Robinson told the club's official website.
"It is no secret I have wanted to bolster the midfield since we suffered the long-term injuries to Luke Chadwick and Stephen Gleeson and by bringing in Ryan Harley and now Chris Lines, we believe we have the creative spark we have been missing.
"Chris is a talented footballer who scores goals from midfield and I think he will fit in well with our team."
Lines, who has made just six appearances in the npower Championship this season, is set to make his debut Saturday's FA Cup fourth-round tie against QPR at Loftus Road.