Wilson, who was a free agent after leaving Bristol City at the end of last season and had spent time training with United this summer, has joined until the end of January.
He previously played for the club earlier in his career before joining Celtic in 2006, and McNamara told the club website: "Mark brings experience and ability to the squad. The short term deal will give him an opportunity to show there are no fitness concerns.
"He will enhance our squad and his versatility is important. He is comfortable at right back and left back and also gives the option of playing in front of the back four.
"He is the type of player who will help us get control of the ball and settle us down when required and I am delighted he has signed."
Wilson added: "Tannadice holds great memories for me as I had great times here as a young player. I am coming back as an older, more experienced footballer.
"I know I can be a useful asset for Dundee United and I cannot wait to get playing again."