The club confirmed they had dismissed Michel because of "a poor run of results" which has left the team 12th in the Primera Division.
Emery, who had a four-year spell in charge of Valencia and was sacked by Spartak Moscow in November, has agreed to take over on a contract until June 2014.
Former Real Madrid and Spain midfielder Michel was only appointed last February, but has endured a difficult first full season in charge.
Sevilla have lost five of their last seven league games, including a 2-0 loss at Valencia on Saturday.
The 2006 and 2007 UEFA Cup winners have won just six of their 19 league games.
The decision to sack Michel was taken at a board meeting today.
Emery, 41, who coached Valencia from 2008 to last summer, lasted just six months at Spartak, his first taste of managing abroad.
His first match in charge of his new club will be Wednesday's Copa Del Rey quarter-final first leg away at Real Zaragoza.
Meanwhile, Sevilla winger Diego Perotti could be out of action for up to six weeks with a hamstring tear.
Perotti limped out of the defeat to Valencia just 17 minutes after appearing as a 62nd-minute replacement and, after undergoing scans, Sevilla estimate the Argentina international could be missing for between four and six weeks.
That would rule him out of both Copa del Rey ties against Real Zaragoza as well as up to seven league games.