The Serbia international won three Premier League titles and the Champions League during his nine-year spell at Stamford Bridge, which ended in 2017.
“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.”