The 28-year-old started out at Manchester United, where he was a prolific loanee, before moving to West Ham, Stoke and last year Norwich.
Chadwick had been on loan at stadium:mk earlier this season where he scored three goals in an injury-hit spell from October, impressing manager Roberto Di Matteo enough to secure a permanent deal.
"I can't wait to get started again. I really enjoyed it here earlier in the season. I felt really settled even though I was on loan and the supporters were brilliant to me," he said.
"I've got some work to do to get over this (knee) injury at the moment, but I'm looking forward to getting back on the pitch and hopefully helping the team win promotion."