Madrid has not said whether it stopped looking for a full-time replacement for Julen Lopetegui, who was fired on Oct. 29.
Solari, a former Madrid player, was appointed as the interim coach but had not been ruled out as a candidate.
His chances of staying increased after he led Madrid to four straight victories since replacing Lopetegui.
"What I can say is that we are very happy (with Solari)," said Emilio Butragueno, Madrid's director of institutional relations. "He arrived at a very particular moment and has been able to achieve some very good results."
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