The 23-year-old rose through the ranks at the Emirates Stadium, but left last year having failed to make a senior appearance for the club.
He spent most of last season with Ryman League Premier Division side Harrow Borough, but he has now returned to professional football.
"James has been brought in to compete with Ross Worner for the number one jersey," Wimbledon manager Neal Ardley told the club's official website.
"We had him in for training three or four times last season. He played in a behind closed doors match for us and really impressed. James won the Player of the Year award last season at Harrow and four or five clubs tried to get him in on trial."
Shea has also turned out for Dagenham & Redbridge and Needham Market.