Cordero made his debut for Saprissa on 1 September 1991 against Limón, coming on as a sub for Alexandre Guimarães[2] and scored his first goal on 29 December 1996 against Cartaginés.

[3] He has played his entire career for Saprissa, with whom he has won 11 national championships and three CONCACAF Champions' Cup, and was part of the team that played the 2005 FIFA Club World Championship Toyota Cup, where Saprissa finished third behind São Paulo and Liverpool[4] He is one of the most title-winning soccer players in Costa Rica's and Saprissa's history, as well as one of Costa Rica's players with most seasons playing under one single team, with 20 straight seasons with Saprissa.

[2] He made his debut for Costa Rica in a September 1995 friendly match against Jamaica[3] and earned a total of 51 caps, scoring no goals.

[11] His final international was a June 2008 FIFA World Cup qualification against Grenada.

Cordero is married to Sigrid González and they have three sons, Ariel, Julen and Thiago.