The move on Monday came amid reports the team was trying to work out a trade to bring quarterback Carson Palmer from Oakland.
Skelton beat out Kevin Kolb for the starting job under then-coach Ken Whisenhunt in training camp last season. He was hurt in the opener and Kolb took over.
Skelton returned as starter when Kolb was injured, but lost the job due to poor performance. The Cardinals released Kolb earlier and he has agreed to a contract with Buffalo.