U's boss Chris Wilder told BBC Oxford: "He's been battling with James Constable for his position.
"He's honest and hard working but we felt we had to change it about. We're looking for people in that position ourselves. He goes with our blessing."
He added: "We circulated a few names and Southend through [assistant boss] Tommy Widdrington, who knew Midson from their non-league days got in touch, and decided to take a chance on Jack."