The 26-year-old Costa Rica international arrived in Glasgow yesterday to complete his deal to the Parkhead club.
Gamboa, who joined the Baggies in 2014 from Rosenborg, has won 47 caps for his country and played in the 2014 World Cup in Brazil.
He would offer competition to Mikael Lustig and Saidy Janko as Brendan Rodgers’ side get set for their first Champions League campaign in three years.
The Hoops boss has already recruited Scott Sinclair, Moussa Dembele, Kolo Toure and Dorus de Vries to the Parkhead club this summer.
A club statement read: “Celtic are delighted to announce the signing of Cristian Gamboa from English Premier League side West Bromwich Albion on a three-year deal.
“The Costa Rican internationalist has notched up almost 50 appearances for his country and he was a star of the side that reached the 2014 World Cup quarter-finals.
“A pacey full-back with attacking instincts, the 26-year-old has spent the past two years at The Hawthorns after impressing for Norwegian side Rosenborg.”