The Nigerian defender joined FC Tulsa on January 13, 2020. Kwambe has spent his domestic career playing in the NPFL, primarily with Lobi Stars F.C. Kwamba manned the backline for Lobi Stars from 2015-2019, where he was a captain, leading them to an appearance in the 2019 CAF-Champions League.
Before joining Lobi Stars, Kwambe spent 2012-2015 with Sunshine Stars and spent the latter half of the 2015 season on loan with Warri Wolves. Kwambe was a prominent part of Nigeria's 2012 and 2013 Super Eagles squads, and he went with the national team to the 2014 Confederations Cup in Brazil. He scored eight goals over his 61 appearances with Sunshine Stars and Warri Wolves.
Kwambe began his career with Plateau United, scoring five goals in 43 appearances from 2010-2012 as a defender.
A player always looked as loaded with potential, Kwambe was included on Young African Player to Watch lists in 2013 that also included Liverpool FC superstar Mohammed Salah and reigning USL Championship Golden Boot winner Solomon Asante. That potential translated for Kwambe into 18 appearances for Nigeria on the international stage including caps in 2014 FIFA World Cup qualifying and 2015 Africa Cup of Nations qualifying.