The Argentine was only allowed to be in temporary charge for two weeks, after which the club had to make a decision on his future and now it has done so, after four wins from four, MARCA reported.
ESPN initially reported that after the victory against Celta Vigo on Sunday night, Los Blancos sent Solari's new contract to the Spanish Football Federation.
The coach has earned the right to continue in the Estadio Santiago Bernabeu hot seat after beating Melilla, Real Valladolid, Viktoria Plzen and Celta Vigo although it's true that the club had already made its decision before the match at the Estadio Balaidos on Sunday night.
It represents the best start of a Madrid coach in 116 years.
The Real hierarchy wanted to keep the Argentine in charge and will hope that the current run of results can continue instead of having to scour the market for a new coach after the departure of Julen Lopetegui.
Four wins in a row, 15 goals scored and only two conceded mean that Solari has quelled any doubts and managed to wriggle himself free of the 'interim' label.
Madrid is now sixth in La Liga, four points behind leader Barcelona which was beaten 4-3 by Real Betis at the Camp Nou on Sunday.
The Champions League holder is joint top Group G with Roma, which it visits on October 27.