"From him, I have received a very big mission and legacy to pass on and I intend to do just that", Aiyawatt Srivaddhanaprabha said in a tribute to his father, Vichai, who died with four other people when his helicopter spiraled out of control as it left the stadium following a Premier League game on Saturday.
Leicester have also opened a book of condolence in memory of Vichai in a marquee at the stadium.
Srivaddhanaprabha led Leicester City to become Premier League champions in 2016.
The helicopter crashed in flames in a auto park next to the soccer club's stadium shortly after it took off from the pitch following a Premier League game on Saturday night.
"I was terribly shaken by the news". His positivity and ability to make everybody love him was clear for all to see.
The Italian coach had taken over from Nigel Pearson, who managed the club in two spells from 2008-10 and then from 2011 following Vichai's take over the previous year.
The season after winning the title, Ranieri was sacked as Leicester manager in February 2017 with the club one place above the relegation zone.
"The leadership and managerial processes he instilled and encouraged within Leicester City over a sustained period of time has borne fruit in such a way that people throughout the world witnessed the impossible by seeing a club win the Premier League in the most incredible circumstances", Pearson said.
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"This most definitely ensured the belief that sporting miracles can happen".
"A manager could not have wished for a better boss", Pearson wrote in a personal letter published on the website of Belgian team OH Leuven, where he has been coach since a year ago.
Leicester's English League Cup match against Southampton, scheduled for Tuesday, had been canceled, while games involving the club's women's team were also called off in wake of the crash.
A minute's silence will be held ahead of the 3pm kickoff at the Cardiff City Stadium, and both sets of players will wear black armbands.
"It is with extreme difficulty that I write to express and offer my honest condolences and support to the Srivaddhanaprabha and wider King Power family", Pearson said in a statement on Leuven's website.
"Formal identification of the four other people, who are believed to be Nusara Suknamai, Kaveporn Punpare, Eric Swaffer and Izabela Roza Lechowicz, is still being actively progressed", the police added.
Meanwhile, the Air Accidents Investigation Branch (AAIB) continue to conduct its investigations as it tries to establish what caused Saturday's tragedy.