Mesa only traded the Canary Islands for south Wales in July 2017 in a deal worth around £11m, but he failed to make the desired impact in the Premier League and featured in just 11 games out of a possible 24 for the Swans.
With Mesa seemingly not fancied by new manager Carlos Carvalhal, a Swansea statement explained that having other strong midfield options is what led the club to agree to let the player leave.
Ki Sung-yueng, Tom Carroll, Leroy Fer, Sam Clucas and Renato Sanches will continue battling for those midfield places at the Liberty Stadium.
Mesa now joins a Sevilla side currently sixth in La Liga, with a two-legged Champions League Last 16 tie against Manchester United coming up in February and March.
The 28-year-old, who had never played outside Spain before joining Swansea, represents the second signing of the day for Sevilla after the earlier capture of former Watford wing-back Miguel Layun from Porto.