Mohamad said the ex-leader, who ruled for 17 months, would "lead the country's recovery strategy, to achieve the best economic impact, and restore the lives of the people" in the virus-battered country.
Muhyiddin resigned as the Southeast Asian nation's eighth premier on 21 August after several coalition allies withdrew their support for him, ending his razor-thin parliamentary majority.
He took office in March last year, rising to power in time for the pandemic to break out in Malaysia.
Though at first successful in curbing the virus with heavy restrictions, Muhyiddin faced growing public anger over his administration's inability to contain outbreaks of Covid-19 variants.
Malaysia has recorded more than 1.8 million infections since the beginning of the pandemic, with a current rate of about 20,000 new cases and hundreds of deaths every day.
Muhyiddin's fall saw Ismail Sabri Yaakob, a senior leader in his coalition, take over.
Backed by support from Muhyiddin and his allies, he then reshuffled the cabinet, keeping many of the ex-premier's allies on board.