"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.
Steve Perryman, director of football at Exeter City added: "As much as we're devastated as a club we're thinking about his lovely wife and his children, he was a great family man.
"Unbelievable news for us, we've got to get on with it, I know that and the club is just taking stock at the moment and make sure that everything we do is with the wishes of the family.
Stansfield's death tragic - Johnson
"He was the engine of our train, he joined us when we were in the conference, and ended up with us in League One in a very good state and a lot of that was to do with this lads personality.
"I saw the faces of the players after [they were told], and they were absolutely devastated, this is a true team player, a great friend, and they've lost a wonderful person."
Dave Bennett, chairman of Exeter City supporters club said: "It's absolutely tragic, a young man in his prime and taken away like this.
"Nothing can take away the shock of last night of hearing it after the game, it was just dreadful news.
"Everyone loves a striker that gives 100% every game and that's exactly what Stanners did, he ran for 90 minutes non-stop and he gave everything to this football club.
Fans' 'shock' at Stansfield news
"They were still chanting his name last night before this news broke and I think that shows how popular he was here."
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."
Bookmark with:
What are these?