The actress and television host, whose mother died of surgery complications in early September, will also be granted ownership of Joan’s $35 million condo in New York.
The publication also reported that Melissa’s teenage son Cooper, 13, has been given his own bequest although details have not been disclosed.
Shortly after Joan’s cause of death was confirmed, Melissa, 46, took to Twitter to express her sadness.
“In response to NYC’s Medical examiner’s report, we continue to be saddened by our tragic loss,” she wrote. “No further comment at this time.”
Joan passed away on 4 September at the age of 81 while she was being operated on, with doctors ruling that the comedienne died as a result of brain damage caused by a lack of oxygen. Her death was classified as a “therapeutic complication”, which means it was a known risk of the procedure.
As requested by the late television personality, Joan’s funeral was the “huge showbiz affair” she had always wanted.
“I want it to be Hollywood all the way,” she wrote in her 2012 book I Hate Everyone … Starting With Me. “I want Meryl Streep crying, in five different accents… I want a wind machine so that even in the casket my hair is blowing just like Beyoncé’s.”
The funeral took place at the Manhattan synagogue three days after Joan passed away, with scores of celebrities paying their respects and paparazzi documenting the high-profile event.
Whoopi Goldberg and Sarah Jessica Parker were some of the first attendees to arrive, followed by Joan’s Fashion Police co-hosts Kelly Osbourne and Giuliana Rancic who walked into the Temple Emanu-El hand-in-hand.
Joan, who was known for her sharp tongue and acerbic wit, had previously joked that dying of natural causes was boring.
“It’s the grand finale, act three, the eleven o’clock number – make it count. If you’re going to die, die interesting! Is there anything worse than a boring death? I think not.”