The Rosenborg right-back is thought to have completed a medical ahead of a £1.8million move to the Hawthorns and will be unveiled as West Brom’s latest signing.
Gamboa attracted the interest of Premier League clubs after helping Costa Rica reach the quarter-finals of the World Cup, qualifying as winners from Group D ahead of Uruguay as England and Italy suffered elimination.
Hull City were also linked with the 24-year-old, but Albion look to have managed to land another defensive recruit this week.
Liverpool full-back Andre Wisdom has already joined on a season-long loan and flew out to the club’s pre-season training camp in Sacramento, California.
New manager Alan Irvine has been busy in the transfer market also bringing in Joleon Lescott, Chris Baird, Craig Gardner and club record signing Brown Ideye.