It had been reported in the Dutch media that the legendary former Netherlands striker had been suffering from heart palpitations following the death of his father in July.
The problem initially forced him to miss last month's Eredivisie clash at Dordrecht, before the club allowed him more time to recover.
Recent reports suggested Van Basten would not return to the role, but the club confirmed on Monday that the 49-year-old would be back at the training ground this week.
"We are very pleased with the current developments," said AZ director of football Earnest Stewart. "Marco has continuously indicated that after his period of calm that he would like to return to training and that was again shown during the discussions on Sunday and Monday.
"With the medical staff giving the green light a return was decided."
Former Heerenveen coach Van Basten replaced Dick Advocaat during the close-season and will hold a press conference upon his return on Tuesday.