Ivanovic was a free agent after leaving Russian side Zenit Saint Petersburg at the end of last season.
The 36-year-old Serbia defender previously spent nine years in England with Chelsea, where he won three Premier League titles, three FA Cups, one League Cup, one Europa League and the 2012 UEFA Champions League.
Ivanovic joined Zenit from Chelsea in January 2017 and won two league titles and one Russian Cup at the Gazprom Arena.
Ivanovic is West Brom manager Slaven Bilic’s sixth summer signing after Grady Diangana, Matheus Pereira, Cedric Kipre, David Button and Callum Robinson.
Ivanovic told the club's official website: "The Premier League is the best league in the world. 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."
West Brom lost their opening game of the season 3-0 at home to Leicester City last Sunday.
The Baggies travel to Goodison Park to take on Everton in their next top flight outing this weekend.
Ivanovic is Serbia’s most capped player with 105 international appearances to his name.
