According to a statement on the club's official website, the 42-year-old Solari has now been handed a two and half years contract as first team manager, after arriving on interim basis from the junior team- Castilla.
"Real Madrid's board of directors met today and made a decision to name Santiago Solari as first team coach until June 30, 2021", the club announced in a statement.
Real Madrid has now scored 15 goals and conceded just two under Solari.
Last season's Champions League winners are four points behind leaders Barcelona in the La Liga table.
En medio de incendios, buscan más de 200 desaparecidos en California
Dos mil estructuras ya han sido destruidas y hay "inminente peligro" de incendio para 15 mil viviendas y dos mil edificios. Tengo mi ropa y una mochila, y eso es básicamente todo", dijo.
The last of those, a 5-1 thumping at the hands of Barcelona, proved the final straw for club president Florentino Perez but the team have rebounded under their new coach.
Real Madrid will hope to maintain their winning streak when they take on Eibar after the worldwide break (November 24, 12pm United Kingdom time). "We are very happy with how things have gone". It's a great opportunity.
After the global 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.
In the meantime Solari, who had previously been in charge of Madrid's reserve side, began achieving results that his predecessor had failed to accomplish.
Following Real's 4-2 win over Celta Vigo on Sunday, Solari said: "The important thing is to do what is necessary for the good of the team, everything else doesn't matter".