Billionaire Vichai Srivaddhanaprabha, two members of his staff, the pilot and a passenger were killed when the aircraft spiralled out of control and crashed in a fireball on Saturday.
It had just cleared the King Power Stadium when it came down at 20:30 BST.
The Duke of Cambridge said he was lucky to have known Mr Vichai, describing him as a dedicated family man.
Leicestershire Police said it believed the other people killed in the crash to be two members of Mr Vichai’s staff – Nursara Suknamai and Kaveporn Punpare – pilot Eric Swaffer and his partner Izabela Roza Lechowicz.
Mr Swaffer had over 20 years’ flying experience as a private jet and helicopter pilot.
His career included flying helicopters for live media broadcasting including Channel 4’s The Big Breakfast and the Virgin Radio traffic helicopter. Mr Swaffer’s friend Lucie Morris-Marr said he was a “veteran in the field” and would have done all he could to prevent lives being lost in the crash. She described him as a “funny and vivacious” man who was in an “aviation love story” with Ms Lechowicz.
“Not many people get to work and travel with their soulmate, travelling the world going to glamorous places,” she said.
The couple were professional pilots who lived together in Camberley, Surrey. Ms Lechowicz moved to the UK from Poland in 1997.
In a statement, the Polish embassy said: “With great sadness, we received the news about the death of Izabela Lechowicz in the Leicester catastrophe.
“She was a great pilot, winner of the #Polka100 contest. It contributed to the creation of a positive image of Poland in the Uk.
Mr Vichai, 60, who was married and had four children, bought Leicester City for Ã‚Â£39m in 2010.
Under his ownership the Foxes won the Premier League in 2016, having started the season as 5,000/1 outsiders.
In a statement, Leicester City said the club’s thoughts were with “the Srivaddhanaprabha family and the families of all those on-board at this time of unspeakable loss”.
Prince William, who is president of the FA, said Mr Vichai made a big contribution to football, adding that Leicester City’s Premier League title-winning season “captured the imagination of the world”.
“He will be missed by all fans of the sport and everyone lucky enough to have known him,” he said.
Former England and Leicester striker Gary Lineker tweeted to say he was “deeply saddened” to hear of Mr Vichai’s death.
Speaking outside the stadium, club ambassador Alan Birchenall said Leicester City owed “everything” to Mr Vichai.
“We wouldn’t have won it [the Premier League] without him,” he said. “We wouldn’t have got near it without him.
“There won’t be a dry eye among any of the staff today.