Former England midfielder Barry, 38, was a free agent, with his contract at The Hawthorns having expired in June.
"Barry is doing very well now and is out there running again and on the way back to fitness," boss Slavan Bilic told the club website.
"It is our plan to sign him again when he has done that. He is a very valuable figure and his experience is important.
"We have many new players to the club and young players who have not much experience and it is important that you are able to have experienced players available to help them when the going gets tough."