Former Arsenal youngster Shea, 23, has joined from Harrow Borough and 20-year-old McDonnell arrives from Basingstoke Town.
Ardley told the club website: "James has been brought in to compete with Ross Worner for the number one jersey. 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.
"Joe was outstanding in a match for the under-21s against Charlton last season and it was one of the best goalkeeping performances that I had seen. He came in and trained regularly with us last season and looked like a first-team goalkeeper.
"We are out there recruiting and we felt that if we did not get Joe and start trying to develop him then someone else would. We are delighted that he has come in to be a part of our under-21 set-up for next season."