The 19-year-old striker had two loan spells with the League One outfit last season, scoring four goals in 14 appearances.
Manager Karl Robinson has said that he is happy to complete the signing of Bamford.
"Patrick was my number one target and you don't always get your number one target," he told the club's official website.
"He is the one I have been waiting for all summer, I could have brought players in over that time, it's a risk to put all of your eggs in one basket but on this occasion it was worth the gamble. Thankfully we got the deal done and we're extremely fortunate to have his services for the next few months.
"When I watch Patrick play I see him do things which other players find very hard to do, he is still very young but he is a tremendous talent and when you work with him every day in training you see what quality he possesses."
Bamford joined Chelsea from Nottingham Forest in 2012.