The 22-year-old has been on trial with the U's during pre-season, having left Anfield this summer after 13 years.
George has had loan spells with Tranmere and Carlisle, where he made four League Two appearances in 2017-18.
Colchester head coach Steve Ball said: "The modern goalkeeper, with how we want to play, has to be comfortable in possession and he ticks all the boxes."
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