The player joins the 'Baggies' for a fee of around £4 million and has signed a three-year deal with the club.
He decided to leave Swansea, who like West Brom were relegated from the Premier League last season, after making just 36 appearances for the club in six seasons.
However, he did spend a successful loan spell at Championship outfit Leeds United in 2016-17, where he played 45 times in the centre of defence for the Yorkshire club.
West Brom were in need of strengthening their defensive ranks after selling Jonny Evans to Leicester City and releasing his Northern-Irish team-mate Gareth McAuley.
Speaking to the club's website, Bartley admitted that manager Darren Moore was a big reason in his decision to go to the Hawthorns.
"After speaking with Darren (Moore) I knew this was the place I wanted to be.
"He let me know his ideas for the season and the next few years, his ambitions for the club and he told me about the fan base and the facilities. I'm hoping to be involved quickly."
The defender is the club's second signing of the summer, alongside Sam Johnstone who joined from Man Utd.