Regragui took Morocco to the World Cup semi-finals in Qatar in 2022 and was also at the helm in January when Morocco lost in the final of the Africa Cup of Nations.
He quit citing exhaustion.
Mohamed Ouahbi will take over as coach, reports said. He was in charge when Morocco won the U-20 World Cup in Chile last year.
The 50-year-old Regragui had been the target of supporter criticism despite a stellar record of 36 wins in 49 matches with eight draws and only five losses since taking over in September 2022.
During that time Morocco recorded the best achievement by an African country at the World Cup and set a new world record for the most successive wins by a national team - a total of 19 between June 2024 and last December.
According to multiple reports, Regragui had wanted to quit after Morocco lost a controversial Nations Cup final to Senegal in January in a tournament they hosted and where they were hoping to end 50 years without success in the continental championship.
He said he was worn out after almost four years in the post but had been persuaded to delay his decision until Morocco had found a successor.
Morocco play two friendly internationals later this month as they prepare for the World Cup, which kicks off in June. They take on Ecuador in Madrid on March 27 and Paraguay in Lens, France four days later.
At the World Cup, Morocco compete in Group C with Brazil, Scotland and Haiti.
In a message to Regragui on social media, Morocco captain Achraf Hakimi said: "Thank you for the incredible work you did leading the Moroccan national team.
"Your leadership, passion, and vision inspired not only the players, but also an entire country and millions of fans around the world."
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