Jimenez was dismissed after Tuesday's home draw with basement side Xerez and Sevilla have tapped Alvarez, a member of the club's technical staff, after an attempt to lure Luis Aragones was rejected by the former Spain coach.
The Andalusians are fifth in La Liga and the main task for the new coach, previously assistant under Jimenez and former bosses Joaquin Caparros and Juande Ramos, will be to secure one of Spain's four spots in Europe's elite club competition.
Sevilla are also through to May's King's Cup final against Atletico Madrid.
"It's a dream ... the day I have been waiting for is finally here," Alvarez, 54, whose first match in charge will be Sunday's La Liga game at Villarreal, told a news conference.
"I am full of excitement, desire and confidence to take this project forward," he added. "It was my life's ambition and today I have seen it become a reality."
Sevilla suffered a surprise Champions League exit to CSKA Moscow last week and Tuesday's draw with Xerez meant they had failed to win in seven matches in all competitions.
Alvarez said his immediate priority would be to lift the players' spirits and convince them they were capable of winning all their remaining matches and at the very least securing fourth place in the standings.
TEN FINALS
"We have 10 matches left, like 10 finals, and there is time to get back to playing the ball around nicely, pushing forward and playing in the opposition half," he said.
"You have to be (optimistic) and trust that we will at least secure fourth place, because the team is capable of winning the 10 matches we have left."
Sevilla have 45 points from 28 matches and are two points behind fourth-placed Real Mallorca. Real Madrid lead Barcelona on goal difference with both on 71 points, while third-placed Valencia are on 53.
Sporting director Ramon Rodriguez said at the same news conference that club president Jose Maria del Nido had indicated he was hopeful Alvarez would remain in charge two or three years longer "if everything goes well".
Local media reported that the talks with Aragones failed because the 71-year-old, who orchestrated Spain's triumph at Euro 2008, was pushing for a contract until the end of next season but Sevilla were unwilling to guarantee he would stay on after the end of this term.
