The trio were appointed on a temporary basis at the end of November, after Racing parted company with Argentine Hector Cuper when the side slid to the foot of La Liga, and they have brought some hope back to the troubled club.
"After analysing the situation the club have ended the uncertainty prevalent on the Racing bench, giving the coaches the stability needed to successfully develop their work," Racing said in a statement.
Since replacing Cuper, who had managed only one win in 13 outings, Gonzalez and his colleagues have secured one win and two draws in La Liga and guided Racing past Rayo Vallecano into the last 16 of the King's Cup.
Racing have been in financial and institutional turmoil for much of the year since Indian businessman Ahsan Ali Syed took over ownership of the club.
The club accused Ali Syed of failing to honour his commitments and slipped into administration in July with debts of over 33 million euros.
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