Thai billionaire Vichai, 60, was one of five people killed in Saturday's crash, and is credited with leading Leicester's meteoric rise from English football's second tier when he took over in 2010 to champions for the first time.
"Struggling to find the right words," Vardy posted on Instagram alongside a picture of him and Vichai smiling.
"But to me you are legend, an incredible man who had the biggest heart, the soul of Leicester City Football Club.
"Thank you for everything you did for me, my family and our club. I will truly miss you.... may you rest in peace... #theboss."
Struggling to find the right words....but to me you are legend, an incredible man who had the biggest heart, the soul of Leicester City Football Club. Thank you for everything you did for… https://t.co/FzTaXVejUg
Vardy plucked from the obscurity of non-league side Fleetwood Town in 2012, represented the shrewd investment that characterised Vichai's ownership.
Another impressive signing Harry Maguire, bought from second-division Hull less than a year before starring for England at this summer's World Cup, thanked Vichai for his support during his time in Russia with the Three Lions.