Thai billionaire businessman Vichai, 60, and four others died when their helicopter crashed and exploded outside the King Power Stadium after a Premier League game against West Ham.
William, President of the English Football Association, and Kate met Vichai's wife, son and daughter at a dedicated tribute site bedecked in flowers, scarves and flags set up in his memory near where the accident occurred.
As they approached, the couple bowed their heads and Kate laid a bouquet of flowers. An accompanying hand-written note read: "To Vichai, and all those who have lost their lives in this terrible tragedy, you will be sadly missed. Our sincere condolences to the city."
It was signed "William" and "Catherine".
The royals, officially known as the Duke and Duchess of Cambridge, then met Leicester manager Claude Puel, a group of players including club captain Wes Morgan, England striker Jamie Vardy and goalkeeper Kasper Schmeichel as well as club supporters and volunteers.
Vichai bought the unheralded central England side in 2010 and went on to stun the soccer world by beating odds of 5,000/1 to win the Premier League title in 2016.
"Their Royal Highnesses knew the Club’s Chairman, Vichai Srivaddhanaprabha, and wanted to visit the city to recognise the warmth and compassion that the people of Leicester and fans of Leicester City Football Club have shown in reaction to the accident," William's office said in a statement.
The couple were later due to go to the University of Leicester to meet representatives of local charities and educational programs that Srivaddhanaprabha and the club have supported.
Earlier this month, British air accident investigators looking into the cause of the helicopter crash said they were focusing on a problem with the tail rotor system.
