The 24-year-old joins from Norwegian side Rosenborg and has signed a three-year contract with Alan Irvine's side after his work permit application appeal was accepted.
The 24-year-old right back, who started in all five of Costa Rica's fixtures at the World Cup this summer, has signed a three-year deal with Alan Irvine's side, after his work permit application was approved by a Football Association (FA) appeal panel on Tuesday.
“As I commented the other day, it would have been amazing if Cristian had not been granted a work permit and we’re obviously satisfied with today’s outcome," Irvine told the club's official website. “Cristian is a player I was extremely impressed by during the World Cup.
"We faced stiff competition from other Premier League clubs for his services but we've managed to convince Cristian that West Bromwich Albion is the best club for him to join. Cristian is a quick, aggressive defender with good energy levels. He gets up and down the pitch really well and we believe he will continue to improve."
Gamboa becomes West Brom's eighth signing this summer following the arrivals of Brown Ideye, Craig Gardner, Joleon Lescott, Chris Baird, Sebastien Pocognoli, Jason Davidson and Andre Wisdom, who has joined on a season-long loan from Liverpool.
Like other Ticos, Gamboa benefited from Costa Rica's deep World Cup run. In addition to the right back's Premier League signing Keylor Navas' move to Real Madrid and Jose Miguel Cubero's signing with Blackpool are official while other transfers are still being rumored for several members of the national team's midfield.