The former Yeovil and Hereford player scored seven goals in 19 appearances for Exeter last season.
The League One side made a statement on its website after a 3-2 home Carling Cup defeat by Ipswich on Tuesday.
"It is with great sadness that Exeter City Football Club have to confirm the news that Adam Stansfield passed away this evening," it said.
606: COMMENT
He always gave 100% and more - a real team player. Only last night the crowd were singing 'There's only one Adam Stansfield'
Exeter007123
"Our thoughts are with his wife, family and friends at this time."
Exeter said it would open the Big Bank gates at St James Park from 0930 BST on Wednesday for fans who wish to pay their respects.
The Tiverton-born forward, nicknamed 'Stanno', joined Hereford on a free transfer in 2004 and two years later moved on to Exeter, where he made more than 150 first-team appearances, scoring 39 goals.
Stansfield started his professional career at Yeovil under manager Gary Johnson who drafted him in from Sunday league football.
"It's absolutely tragic. I heard it first last night and it was a total shock," Johnson told BBC Somerset. "It's unbelievable that such a nice lad has gone so soon.
"He's probably one of the hardest working footballers I've ever worked with.
"He was very popular with the fans for the simple reason they could see that he always gave everything. They'll remember him for his heart, he was all-action and never gave up on anything."
Source: BBC Sport
Source: BBC Sport