The 36-year-old has signed a one-year contract, having been a free agent after leaving Zenit St Petersburg.
Ivanovic joins after the Baggies 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," he 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.
"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."
Ivanovic won three Premier League titles, three FA Cups, the Champions League, Europa League – he scored the winner in the final against Benfica in 2013 – and the League Cup during nine years at Chelsea.
He is also Serbia's most capped player with 105 appearances.
Baggies boss Slaven Bilic 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."