Spanish rules state that an interim coach can not be in charge for more than two weeks so Madrid had to appoint Solari - or an alternative - to avoid punishment.
This now means that the next Madrid derby will have two Argentine coaches at the helm.
The club, who confirmed Solari's appointment in a brief statement on their website, were ninth when he assumed control and they are now sixth, four points adrift of leaders Barcelona.
This was after the club's poor run of form culminated in a painful 5-1 El Clasico defeat by FC Barcelona.
Israeli defense minister announces resignation protesting Gaza truce
But late Tuesday, Hamas and other military groups issued a joint statement saying they had accepted an Egyptian cease-fire. But the political fallout from the ceasefire agreement could be huge for Israeli Prime Minister Benjamin Netanyahu.
Usyk: Fight with Bellew to be 'unbelievably lovely
The Briton responded: "He can give me that insane Ukrainian look, so I just gave him a insane Scouse one back". He didn't come in there to just pick up his pay cheque and just quit. 'Eddie Hearn stuck by me all the way.
Prince Charles to share birthday celebrations with Barry man
The photos were scheduled to be released on November 14 when he turns the milestone age, but they leaked early on November 13. In the front row, Prince Charles bounces Prince George on his lap as he sits next to Camilla and Princess Charlotte .
Asensio said of the new manager: 'The results have been better [since he took charge] and football is like that.
The Spanish press had urged Real to appoint the former Castilla "B" team coach.
After the worldwide break, Madrid´s generous run of games continues with league matches against Eibar, Valencia, Huesca, Rayo Vallecano and Villarreal before Christmas, none of whom now reside in La Liga´s top half.
Solari won two league titles and the 2001-02 Champions League during five years at the club as a player and was in charge of the reserve side before taking control of the first team on October 29. "I don't just say that now as coach of the first team".
Antonio Conte, Mauricio Pochettino, Jose Mourinho and Joachim Low had all been linked to the position.