Sources have told ESPN Mexico that he has signed with the club for two years.
"I will try to live up to your expectations," Aguirre said in a statement. "I will try to return the affection that fans without a doubt will give us and have given the team for so many years through [winning] titles."
Aguirre comes into a club that won the 2019 Apertura title, is still the reigning CONCACAF Champions League holder and boasts one of the most expensive squads in the Americas, with players such as Vincent Janssen, Jesus Gallardo, Maximiliano Meza and Carlos Rodriguez.
Former coach Antonio Mohamed was released from the club on Nov. 25, after Rayados fell to minnow Puebla in the play-in round of the Liga MX playoffs.
Aguirre had previously said in interviews that a return to Mexico didn't interest him at this point in his career, indicating that he preferred a job in Major League Soccer or in the Japanese League.
But it seems the draw to go back to was too strong to deny.
"Firstly, to go back to my country and be amongst my own [people]. I need that shelter, that carne asada and beer with friends, speaking the same language. I'm from there, I grew up there, I trained there, I was a player, a coach there and the only thing that I did, during 20 years was miss my homeland," Aguirre said.
He coached his country at the 2002 and 2010 World Cups, with Mexico going out at the round of 16 stage on both occasions.