Solari has led Real to four wins out of four since being installed on a caretaker basis following Lopetegui’s abrupt sacking last month.
The upturn has left Madrid only four points adrift of league leaders Barcelona and on the brink of qualification for the last 16 in Europe.
“Everything is in order. Real Madrid have worked out his contract and there are no problems,” the Spanish football federation stated.
Solari, who spent five years playing for Real, was promoted from his role in charge of Castilla, the club´s B team, after Lopetegui had overseen a miserable run that included just one victory in seven games.
“He has done excellently, We are very happy with how things have gone.” Madrid club director Emilio Butragueno said on Sunday night.
Santiago Solari, who rejected any form of comparison between himself and former Real Madrid manager, Zinedine Zidane, stating in his opening press conference that he was open to keeping the job full-time.
Solari has played down the comparisons with Zidane, who commanded instant respect owing to his glittering playing career and long-established status at the club, enhancing his status as a Real legend by winning three consecutive Champions League crowns.
“He’s one of the greatest things we’ve ever had at this club,” Solari said last month. “He’s very calm, a great coach and nobody can compare to him.”
Solari was only allowed two weeks as an interim coach according to Spanish regulations, meaning Sunday´s trip to Celta Vigo was always likely to precede a decision on his future.
Antonio Conte, Mauricio Pochettino, Jose Mourinho and Joachim Low had all been linked to the position, with fresh approaches still possible next summer.