AC Milan have completed the permanent signing of defender Cristian Zapata from Villarreal for an undisclosed fee.
Millwall have yet to choose a new manager amid speculation former Liverpool defender Markus Babbel is set for the job.
Clifford put pen to paper on Friday morning before training with his new team-mates and the 20-year-old midfielder will be available for selection when the U's host Scunthorpe on Saturday.
Clifford played 45 minutes for Chelsea's Under-21 side on Thursday night - a game that Joe Dunne attended - and the Colchester boss is pleased to have got the player on board.
He told the official website: "He is an exciting youngster with plenty of ability that we will benefit from in the coming weeks.
"He has been in Chelsea's first-team squad on occasions already and I have been very impressed with what I've seen of him.
"I'm really glad that we have secured his services and I'm sure that he will add to the quality we already have in the squad."