Ivanovic made more than 350 appearances for Chelsea and won nine major titles with the London club before leaving for Russian side Zenit Saint Petersburg in 2017.
He returns to England's top flight as Slaven Bilic's sixth signing since West Brom's promotion, following the arrivals of Grady Diangana, Matheus Pereira, Cedric Kipre, David Button and Callum Robinson.
"I'm so happy to be back," Ivanovic told West Brom's website.
"I know Slaven from before. He's amazing and I hope together we're going to be a success. He understands football and looks like a guy who everyone wants to play for.
"I missed English football ... I looked to be back in the previous year but it didn't happen, so now I'm happy to be here and I'll try and do my best. I can give something more. I'm completely different... I'm ready for the challenge."
Ivanovic's arrival is a boost for West Brom, who conceded three goals without reply in a Premier League defeat by Leicester City on Sunday.
They host Harrogate Town in the League Cup later on Wednesday before travelling to Everton in the league on Saturday. (Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford )