Mr Srivaddhanaprabha was among five people killed when the aircraft came down outside the King Power Stadium on Saturday, shortly after the team's 1-1 draw with West Ham.
Leicestershire Police said the others who died were Nursara Suknamai and Kaveporn Punpare, who were members of Mr Srivaddhanaprabha's staff, as well as pilot Eric Swaffer and passenger Izabela Roza Lechowicz.
The club described their chairman as "a man of kindness, of generosity" and said "Leicester City was a family under his leadership".
He led the Foxes to the Premier League title in 2016, defying the 5,000/1 odds they faced at the start of the season.
Leicester goalkeeper Kasper Schmeichel, who was reported to have witnessed the aftermath of the tragedy, shared a heartfelt Instagram post in which he told of his devastation at Mr Srivaddhanaprabha's death.
"It is difficult to put into words how much you meant to this football club and to the city of Leicester," he said. "Never have I ever come across a man like you. So hard working, so passionate, so kind and so generous in the extreme.
"You changed football. Forever! You gave hope to everyone that the impossible was possible. You literally made my dreams come true."
Teammate Jamie Vardy called Mr Srivaddhanaprabha a "legend".
He said on Instagram: "Struggling to find the right words, but to me you are a legend, an incredible man who had the biggest heart, the soul of Leicester City Football Club."
Football clubs around the world shared messages of support on social media, hailing the Leicester owner for his legacy.
Mexican club Tigres UANL said Mr Srivaddhanaprabha had "showed the world in 2016 that it is possible to believe in miracles".
French club Paris Saint-Germain said it was "shocked and saddened by the tragic events", while Barcelona tweeted: "Our thoughts are with the whole @lcfc family."
Pundits also paid tribute, with Gabby Logan saying in reference to Schmeichel: "There are not many players and certainly fewer clubs who could boast players who can write this about their relationship with the owner."
Leicester City Council said Mr Srivaddhanaprabha had "made a huge contribution" to the city, adding: "We would like to pay tribute to him for all he has done."
Leicester South MP Jonathan Ashworth said it was "awful news", and added: "Our thoughts are with the loved ones of all who lost their lives in the helicopter crash. Khun Vichai was loved and respected hugely across Leicester."
Simon Cole, Chief Constable of Leicestershire Police, praised the impact Mr Srivaddhanaprabha had on Leicester as a city, as well as the football club.
He said on Twitter: "Vichai was a generous man, who gave so much to Leicester in so many ways, including millions of pounds to charity, but he also gave hope, and delivered a seemingly impossible sporting dream. May he rest in peace."
Wembley showed its support for the club as the famous arch above the national stadium was lit in white and blue to honour the East Midlands side.
Tony Fernandes, former chairman of Queen's Park Rangers, called the news "tragic" and said: "His spirit will live on with his tremendous son. Vichai will allow us all to dream. He made the dream a reality and that will allow all of us to continue to dream the impossible and never give up. Farewell my friend."
A condolence book will be opened at the King Power Stadium on Tuesday for fans and well-wishers to pay their respects, Leicester City said.