The striker, a champion with Cheltenham Town in 2016, has put pen to paper on a contract.
Wright played a key role as the Robins won the division two years ago.
Now managed Tim Flowers thinks he can have an equally important part to play as the Moors look avoid a struggle down the bottom.
Flowers took over from Mark Yates a fortnight ago with the manager filling the vacancy at Macclesfield Town.
He has a number of transfer targets and wants to build a squad which can push on after their season near the bottom last term.
Wright, 33, has also played for Wrexham, Histon, Cambridge United and Kidderminster in Non-League.