The Serbian defender last played for Zenit Saint Petersburg, where he featured 31 times for the Russian club last season.
Now a free agent, the 36-year-old has sealed a return to the Premier League and will add top flight experience to Slaven Bilic's defence.
The former Premier League and Champions League winner has signed a one-year deal at The Hawthorns and will wear the number 20 shirt.
“The Premier League is the best league in the world,” Ivanovic said.
“I need to challenge myself and I am ready for the challenge. I am really happy to be back playing in the Premier League.
“I hope I am going to be successful here.
“I have a lot of ambition and I want to prove a lot of things. I will give everything for the team.”
Baggies boss Slaven Bilić believes the signing of Ivanović will be a big boost to his squad.
He added: “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.
“So it is not only him, it is him plus the influence he will have on not just defenders but the whole team around him. That's why we targeted him as one of our prime targets.
“It’s a great signing for us.”