Garcia lost his job after a run of 12 La Liga matches without a win left the side precariously placed just one point above the bottom three.
A matter of hours after announcing his departure, the club confirmed their agreement to bring in Contra as his successor.
"Getafe and Cosmin Contra have reached an agreement in principle to be the new coach of the first team for the remainder of the season and two more campaigns," a club statement read.
The 38-year-old was at the club for five years during his playing career, and joins from Romanian outfit Petrolul Ploiesti.
Contra is due to be unveiled at a press conference on Tuesday.
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