The 27-year-old is set to make his debut for the Dons in Saturday's FA Cup fourth round tie against QPR at Loftus Road.
Lines, who started his career with Bristol Rovers, made 47 appearances for Wednesday last season but has only featured six times this term following their promotion to the Championship.
MK Dons boss Karl Robinson told the club's official website: "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.
"Chris is a talented footballer who scores goals from midfield and I think he will fit in well with our team."
Lines added: "I am looking forward to joining MK Dons and hopefully getting some games under my belt."