Former Collingwood CEO Pert, who joined the Demons at the end of 2018, follows former president Kate Roffey who stepped down in September.
It follows an ongoing period of turbulence at Melbourne.
The Demons are expected to confirm his resignation on Thursday, with Pert set to stay on purely as a consultant for Melbourne's bid to build a new training and administration base at Caulfield.
Pert's departure comes as the Demons prepare to hand down the findings into two separate reviews into their operations.
President Brad Green is reviewing the club's board while Melbourne have enlisted former All Blacks manager Darren Shand to look at their football department.
Melbourne have been wracked by turmoil almost since their breakthrough 2021 premiership.
They haven't won a final since - Â suffering straight-sets finals exits in 2022 and 2023 before missing the top eight altogether this year and finishing 14th.
Queries over their off-field culture have popped up time and time again, and weren't quashed by Pert's extraordinary claim late last year that the club's culture was the best he had seen in 40 years.
Clayton Oliver's off-field troubles, and disgruntled star midfielder Christian Petracca's desire to leave the club following his horror injury in the King's Birthday match, have been among the headline issues.
Joel Smith's long-running anti-doping case, which was made public last year, also cast a shadow over the club with coach Simon Goodwin insisting in March the Demons did not have a drug culture.
Pert's name was in the headlines again earlier this month when he reportedly made contact with multiple clubs to test interest in a potential trade for Oliver.
It resulted in Oliver exploring a move to Geelong before the Demons ultimately ruled out trading the midfielder.
Petracca also committed to the Demons, for 2025 at least, on August 31.
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