Mikel Vesga was born and raised in the Basque city of Vitoria-Gasteiz and joined the local academy Aurrerá Vitoria as a child. He made it all the way to the first team in the Tercera before leaving to join Alavés B in 2013. After just one season Vesga was showing great promise and Alavés wanted to keep him around but he rejected a renewal offer in order to join Bilbao Athletic where he immediately flourished and played a major role in helping the reserves earn promotion to the Segunda. The following summer he was promoted to the first team and made his debut on 21 August, 2016 in 2-1 loss to Sporting Gijon. Vesga would join Gijon in January of the same season in order to play regular minutes and became a fan favorite before returning to the San Mamés. He then left to join Leganés on loan for the 2018/2019 season where he found success once again.
Mikel Vesga is under contract through 2021 and his deal contains a €30 million release clause.