Betis finished bottom of La Liga this season, with their relegation from the Spanish top flight confirmed late last month following Getafe's 1-0 win over Malaga.
Calderon took over from Juan Carlos Garrido in January, but failed to inspire a turnaround at Estadio Benito Villamarin, masterminding just four league wins during his brief tenure with the Seville club.
And Betis have now confirmed that the club have decided to opt for another change following a poor campaign.
A statement on the Betis website read: "Gabriel Humberto Calderon will not be contracted to Real Betis from July 1.
"Both the coach and the club have agreed that the entity needs to renew its sports project to achieve a return to the Primera Division next season.
"Real Betis would like to thank Gabriel Calderon and his entire technical team for their work, enormous effort and involvement to try to reverse the delicate situation they came into four months ago even though, unfortunately, they have not been able to avoid relegation."
Former Betis coach Pepe Mel has been linked with a return to the club after leaving West Brom by mutual consent last week.
