The struggling second tier club, who were relegated from the Premier League in 2012, announced the news on their website on Wednesday.
Gartside oversaw the club's promotion to the Premier League in 2001 and the successful period when they finished in the top eight for four years in a row and also played in the UEFA Cup for the first time.
Former Bolton player and manager Owen Coyle, now manager of Houston Dynamo, said Gartside had always wanted the best for the northern club.
"We were bottom of the league but with Phil's help we kept them safe and had a great run," he told Sky television of the 2010 and 2011 seasons.
Gartside handed over his duties at the club last November, having stepped down from the FA board in 2012.
Bolton are now second from bottom in the second tier and battling reported debts of 172.9 million pounds ($250.45 million).
In January they were given a stay of execution after the High Court adjourned a hearing from the tax authorities who want the club wound-up.
(Reporting by Alan Baldwin, editing by Toby Davis)
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