Betis sacked Juan Carlos Garrido on Sunday after a mere month and a half in charge and Calderon will take over until the end of the campaign with an option for another season if the Seville-based side avoid the drop.
"The coach... has already signed his contract for what remains of this season and one more year if top-flight status is assured," Betis said on their website (www.realbetisbalompie.es) on Monday.
"Without time to lose, Gabi Calderon will take charge of the team (on Monday) and has already prepared a double training session to prepare for (Friday's La Liga) match against Celta Vigo," they added.
A former Villarreal coach, Garrido was appointed at the beginning of December to replace the popular Pepe Mel, who has since taken over at English Premier League side West Bromwich Albion, but failed to turn things around.
Betis qualified for the Europa League after finishing seventh in La Liga under Mel last season and will play Russian side Rubin Kazan over two legs in the last 32 next month.
However, they are five points adrift at the bottom of Spain's top division with just over half the season played and were thrashed 5-0 at home to Real Madrid on Saturday.
It was their fourth defeat in five La Liga games under Garrido and the disgruntled Betis fans chanted for him to be fired and sang Mel's name at their Benito Villamarin stadium.
Calderon, who will be 54 next month, played for Betis between 1983 and 1987 and represented Argentina at the World Cups in 1982 and 1990.
He coached French side Caen and Lausanne in Switzerland before taking charge of Saudi Arabia, whom he helped qualify for the 2006 World Cup in Germany. He has also managed various club sides in the Middle East.
"This has always been my dream," he said on the Betis website after his appointment.
"I did not have a particular date in mind but when a delicate situation like this occurs I come running," he added.
"Betis needs all its supporters. When a loved one is sick we all join forces to help."