"Betis have signed Uruguayan Gustavo Poyet for the next two seasons," the club said in a statement.
The Seville-based side are 14th in the 20-team top-flight with 42 points from 37 matches.
Betis, who are safe from relegation, play their final La Liga game of the season at home to Getafe on Sunday.
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Poyet joined AEK in October but announced last month, on the eve of a Greek Cup semi-final second leg match against Atromitos, that he would be quitting the club at the end of the season.
"What he did was unacceptable, it was not the appropriate time to unsettle the team just hours before the semi-final," club owner Dimitris Melissanidis told reporters last month.
Former Sunderland coach Poyet took over from Traianos Dellas on a deal until the end of the season with the option to renew for another two years.
The former Uruguay midfielder is returning to Spanish football after a 19-year absence.
Poyet, 47, played for Real Zaragoza between 1990-97, winning the King's Cup and the now-defunct European Cup Winners' Cup, before spending four years at Chelsea and then three years at London rivals Tottenham Hotspur.
His first job as coach was with English team Brighton and Hove Albion between 2009-13.
"The club wishes to thank the commitment, professionalism and the love for these colours of Juan Merino and his technical staff," Betis said in their statement.
Poyet will attend a news conference in Seville on Wednesday.
(Editing by Tony Jimenez)
