Alvarez was tapped in late March to replace Manolo Jimenez for the final 10 matches of the campaign and helped the Andalucian club secure a berth in next season's Champions League qualifying round.
He also led them to victory over Atletico Madrid in the King's Cup final.
Sevilla's board of directors had voted unanimously to extend the 55-year-old's contract until the end of next season, the club said.
Alvarez previously served as assistant under former Sevilla bosses Joaquin Caparros and Juande Ramos.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.