The Serbia international won three Premier League titles and the Champions League during his nine-year spell at Stamford Bridge, which ended in 2017.
West Brom marked their return to the Premier League with a 3-0 defeat to Leicester on Sunday.
“The Premier League is the best league in the world,” Ivanovic, 36, told the club’s official website.
“I need to challenge myself and I am ready for the challenge. I am really happy to be back playing in the Premier League.”
West Brom boss Slaven Bilic said: “He’s a great addition for us, a team who are newly promoted in the Premier League. He ticks all the boxes for us.
“He’s done everything in his career — it’s been magnificent. We’re delighted. He adds quality and experience on the pitch and off the pitch.”