The 30-year-old will spend the rest of the season at Craven Cottage and could join the club on a permanent deal next summer.
“Jonno has been a big player for this club and, as you well know, we made every effort to keep him,” West Brom boss Roberto Di Matteo told the club’s official website.
“But eventually we felt the deal on the table was a very good one for us and we decided to let him go. We wish him good luck. He’s been a great servant for this club.”
Di Matteo added: “At the moment, I think we have a very good squad with the players we’ve got. Let’s not forget we have a couple of longer-term injuries with Ishmael Miller and James Morrison. I’m not going to rush into any decisions about another player.”
