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 about 20:30 BST.
Thousands of bouquets and scarves have been left outside the ground.
Leicestershire Police said it believed the dead to be:
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 £39m in 2010.
Under his ownership the club 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”.
The club described Mr Vichai as “a man of kindness, of generosity and a man whose life was defined by the love he devoted to his family and those he so successfully led”.
“Leicester City was a family under his leadership. It is as a family that we will grieve his passing and maintain the pursuit of a vision for the club that is now his legacy,” it added.
A book of condolence will be opened at King Power Stadium from Tuesday morning. The team’s next fixture against Southampton in the EFL Cup, scheduled for Tuesday evening, has been postponed.
Leicester goalkeeper Kasper Schmeichel, who witnesses said ran out of the stadium towards the crash scene, said Mr Vichai had “changed football forever”.
“I cannot believe this is happening. I am so totally devastated and heartbroken,” he added.
Club captain Wes Morgan tweeted: “Absolutely heartbroken and devastated regarding the news of our chairman. A man that was loved and adored by everyone here at lcfc.”
Premier League chief executive Richard Scudamore said: “Vichai was a gentleman who graced the game with his civility and charm and we will miss him enormously.
“His impact on Leicester – the football club and the city – will be remembered forever.”
Paris Saint-Germain, Inter Milan, West Ham United, Tottenham Hotspur, Nottingham Forest and Swansea City were among the football clubs that passed on condolences to Leicester.
The helicopter came down in a car park near the stadium just over an hour after Leicester had drawn 1-1 against West Ham United in the Premier League.
Leicestershire Police confirmed no-one else had been injured and said the Air Accidents Investigation Branch had launched an investigation.
Supt Steve Potter said: “Emergency services were immediately on scene when the crash happened, working to put out the fire and gain access to the helicopter in attempts to reach those inside.
“Despite those efforts, there were no survivors.”
Supt Potter said it was likely to take several days to complete the investigation at the crash site.
Freelance photographer Ryan Brown, who was covering the game, saw the helicopter clear the King Power Stadium before it crashed.
He told BBC Radio Leicester: “The engine stopped and I turned round and it made a bit of a whirring noise, like a grinding noise.
“The helicopter just went silent, I turned round and it was just spinning, out of control. And then there was a big bang and then [a] big fireball.”