"I want to come and help the team," he told the Baggies' official website. "That’s always been the same for me wherever I have played.
"I want to help the team improve, work hard and hopefully add quality."
"There was a big void when we lost 'Fletch' and Gareth will fill that void,” said Pulis.
"He's a fantastic player and I think his attitude towards playing is really gauged by the fact that Everton had offered him a two-year contract to stay there.
"He really wants to play and I'm really looking forward to working with him."
The 36-year-old Barry is five matches short of breaking Ryan Giggs' Premier League appearance record.