The Demons, second-bottom on the ladder in a disastrous season that has included the sackings of chief executive Cameron Schwab and coach Mark Neeld, announced lawyer and former West Coast player Glen Bartlett had been handed the presidency.
"Bartlett was elected to the position by the club's board at a meeting of board members on Friday, and has the support of the AFL, which is assisting with efforts to reinvigorate the club to achieve greater on and off-field success," the Demons said in a statement.
The Demons formed a board nominations sub-committee which includes AFL general counsel Andrew Dillon following the resignations of four board members earlier in 2013.
Further candidates are currently being interviewed.
"I would like to thank the board and the AFL for their support and faith in me," Bartlett said.
Bartlett, who joined the board in July, will take over from interim president Peter Spargo.
Stockdale however, says he's gutted to have missed out on the presidency but has no intentions of pursuing a role on the board.
"I was interested in it (presidency). If I wasn't taking it seriously I wouldn't be disappointed," Stockdale said.
"I'm disappointed not to have a role but I've been around long enough to know that where you've got more than one candidate, only one winner is going to come out of it.
"I don't think it's a good idea to have somebody who has been a high-profile candidate for the presidency going onto the board.
"So I'm content the board should have the opportunity to show it can turn the club around.
"I'd congratulate Glen Bartlett on his appointment. Everything I hear about him is very encouraging.
"I know that (new chief executive) Peter Jackson has a plan to get the best people he possibly can as coach, as football manager and recruitment, right through the club and I'd entirely support that.
"Nothing would give me more pleasure than to see a really good plan turn Melbourne Football Club around."
Stockdale said his campaign attracted lots of public support, particularly on Facebook.
"But the AFL has its own way of doing things," Stockdale told Fairfax Media.
Stockdale's bid attracted support from high-profile figures including former Melbourne Major Events boss Ron Walker.
Walker warned earlier in August the Demons risked becoming the laughing stock of Australian sport if they turned their back on "the most successful treasurer in Australian history".
Former Hawthorn AFL club president Jeff Kennett, who was premier of Victoria when Stockdale was state treasurer, had also made a bid to be Demons' president to succeed Don McLardy who had stepped down in June.
The Demons secured almost $3 million in conditional extra funding from the AFL in June.