The Andalusian side, UEFA Cup winners under Juande Ramos in 2006 and 2007, sacked coach Marcelino earlier this week after they managed only two points from their last seven league games and were eliminated from the Europa League and the King's Cup.
Michel, who coached Getafe until the end of last season, will make his debut away at Real Sociedad on Monday and begin the task of steering the team from 11th in the standings.
Missing out on a lucrative place in the Champions League or Europa League would be a severe blow to the club's finances.
Michel said after overseeing his first training session on Wednesday that it was "unthinkable" that Sevilla were not among the championship leaders and he was confident the squad was strong enough to turn the season around.
"The sensation is one of hope," the sharp-dressing 48-year-old, told a news conference. "I thought I might find players who were emotionally weary but instead we have felt tremendously satisfied.
"We have three months of the season left and we want them to be exciting."
Sevilla's biggest problem is a lack of goals - just 22 in 21 La Liga games - and the club is hoping Michel can get the best out of leading striker Alvaro Negredo and forward Manu Del Moral, with whom he worked at Real Madrid and Getafe respectively.
"This is a change we hope will also serve to alter the negative dynamic that we have," Del Moral told a news conference on Wednesday.
"He [Michel] arrived at Getafe with the club in similar straits and he was able to turn things around and help avoid relegation.
"If I had to choose a coach to change this situation, Michel is without doubt the best equipped."
While Sevilla have been struggling along with other sides who regularly appear in Europe, including Villarreal and Atletico Madrid, leaders Real and second-placed Barcelona have been pulling inexorably away at the top.
The gap in wealth between the dominant pair and their domestic rivals was underlined on Thursday when accounting firm Deloitte confirmed them as the world's richest clubs by income in their annual ranking for a third straight year.
Valencia, who are 11 points behind Barca in third with just over half the season played, were 19th on the Deloitte list, the only other Spanish club to make the top 20.
Champions Barca, chasing a fourth straight title, can trim the gap with Real to four points with a win at Osasuna on Saturday, before Jose Mourinho's Madrid side host fourth-placed Levante on Sunday.
Valencia host struggling Sporting Gijon on Sunday following their elimination at Barca's hands in Wednesday's King's Cup semi-final second leg.
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