And in a show of faith to the Argentine coach, Solari has been handed a deal until 2021 by president Florentino Perez.
The 42-year-old enjoyed an ideal audition for the role, guiding Los Blancos to four consecutive wins in all competitions following Julen Lopetegui's dismissal last month.
But there is scepticism as to how long Solari will remain in the job with Mauricio Pochettino and Jose Mourinho both mooted as possible targets for the summer.
Now the former boss of Real's B-team Real Madrid Castilla has been given the reins of the main side on a permanent basis with the side sitting in sixth place in La Liga, four points behind rivals Barcelona at the top of the table.
The win at Celta gave Solari four wins from four games in charge, with 15 goals scored and just two conceded.
Zidane was initially only a temporary appointment but won the Champions League in his first season and went on to win the European trophy in his next two campaigns, also adding a La Liga triumph, before resigning in May. "When the new coach arrived I started off playing but now I am getting less chances but we'll draw any conclusions when the season has ended".
"It is an inconsistent Barcelona by their own high standards".
Personal situation: "When things are going well, they start saying you're the best but as soon as things go wrong, suddenly you are the worst".
"It's a great opportunity and it's a great club", Solari said.
"In life in general and in this profession we are all just here passing through. Real Madrid have worked out his contract and there are no problems", the Spanish football federation stated.