Ellis, who was forty one, had just finished taking the National League One club for pre-season training in Castleford when he suffered a suspected heart attack.
Attempts were made to resuscitate him and he was rushed to hospital where he was pronounced dead on arrival. He leaves a wife, Melanie, and two young daughters, India and Mia.
"It's a great shock to us all," said Doncaster chairman John Wright.
"He was training with the lads this morning when he had some sort of seizure.
"His heart stopped and he never recovered. We had the physio there and other trained people who tried to give him mouth to mouth straight away.
"He was taken to Pontefract hospital very quickly and given electric-shock treatment but it was no good.
"You wouldn't believe it. There wasn't a fitter coach in the game. He was a fitness fanatic who never asked any of his players to do something he couldn't do himself."
Doncaster Lakers captain Craig Lawton had been training with Ellis when he collapsed.
"Obviously it's just come as a total shock to everyone: Rugby League, Doncaster, everyone who's ever been involved with him," said Lawton.
"Because if you've ever been involved with him you're going to remember it. He was that kind of guy."
The former Castleford and Great Britain winger was the longest serving coach in in professional rugby league, taking over at Doncaster in 1999.
He was a member of the Castleford side which lost to Wigan in the 1992 Challenge Cup final at Wembley and won three Great Britain caps from 1991-94.
Assistant coach Tony Miller has been placed in temporary charge.