The Azulones made the managerial change following a dismal run of results of results which has seem them fall into the relegation dogfight.
Saturday's 2-0 loss at rock-bottom Real Betis left Getafe a point above the drop zone and without a league win since November.
During that run they have picked up just four points from a possible 36 and were also knocked out of the Copa del Rey.
Sporting director Toni Munoz confirmed at a press conference at Monday lunchtime that Garcia was no longer the coach, with the club subsequently announcing they had reached an agreement in principle for Contra to take over the reins.
A statement on www.getafecf.com read: "Getafe and Cosmin Contra have reached an initial agreement for him to be the new coach of the first team, for the rest of this season and for two more years.
"His official presentation will be tomorrow, March 11, at 1300 in the press room of the Coliseum Alfonso Perez."
The 38-year-old Contra spent five years with Getafe during a playing career that also saw him represent the likes of AC Milan, Atletico Madrid, Alaves, West Brom and Dinamo Bucharest.
The former right-back also won 73 caps for Romania before turning his hand to management, with his most recent role being at Petrolul Ploiesti in his homeland.
After taking charge at Petrolul in 2011 - where he was the youngest coach in Romania's top division - Contra helped the club win their first Romanian Cup in 18 years and last season finish third in the league.
That earned them a spot in the Europa League, where they knocked out Vitesse Arnhem before losing to Swansea - then managed by former Getafe boss Michael Laudrup - in the play-off round last August.
Contra will not have long to find his feet back in La Liga as there are only 11 games left this season, and Getafe have a tough-looking fixture list coming up.
After Friday's visit of fellow relegation battlers Granada, the club from the outskirts of Madrid face top-eight sides Athletic Bilbao, Villarreal, Valencia and Atletico Madrid in the space of five games.
Contra's imminent arrival was announced by Getafe following confirmation that Garcia had left the club.
The 41-year-old Garcia took over from Michel in the summer of 2011, signing a three-year deal after buying out his contract at Levante.
Garcia, who had his playing career cut short by injury in 2000, steered Levante into the Spanish top flight and kept them there despite a modest budget before quitting to move to Getafe.
In his first two seasons at the Coliseum Alfonso Perez, Garcia helped Getafe finish 11th and 10th but this campaign the club are embroiled in fight to avoid the drop - something the departing coach desperately hopes they manage to do.
Garcia said: "It's a sad day. I hope with all my heart that Getafe continue in the Primera Division.
"It's been 113 official games in which, taking away the last 12, we've fulfilled the objective.
"The last two years have been very good. In the cup we've knocked out great teams, there were good moments when we beat Barca and Real Madrid. This bad run has been the worst moment.''
Looking ahead, Garcia added: "One door closes and another opens."