Joe Dunne was only appointed as the U's new permanent boss on Thursday morning but Eastmond and Watt join Jabo Ibehre in making it three new faces through the door in his first day at the helm.
Midfielder Eastmond and striker Watt, both 21, have each enjoyed first-team action for the Gunners and also benefited from loan spells away from the Emirates.
Eastmond told Colchester's official website: "The first thing I heard about the move was through my agent and he said Colchester United were one of a few clubs interested. I just want to play games so I said yes to it and I'm looking forward to the new challenge."
Watt added: "It felt good to be training here and the lads made me feel relaxed and welcome. It looks like the manager plays the same formation as I'm used to so it should be good for me.
"I want to fight for my position in the team, keep my place if I get it and do well for the club and for myself. Hopefully, we can play well, pass the ball around, score some goals and push up the table."