The 26-year-old is widely regarded as one of the most talented midfielders in European football, but had his fair share of disciplinary problems during his six years with Valencia.
He spent the second half of last season on loan at Newell's Old Boys, but has now been given the chance to thrive at Sevilla.
"This is an important opportunity for me, that this club has shown their backing for me. I want to work hard every day to earn myself a place in the team and repay the club for the confidence they've shown in me," Inside Spanish Football quotes Banega as saying.
"My main role has always been as a central midfielder, but I feel just as comfortable playing as an attacking midfielder. I feel content playing in any midfield position."
Banega has made 24 appearances for his country.