Vichai's son Aiyawatt has been named as the club's vice-chairman.
Vichai and Aiyawatt were part of the Thai-based Asia Football Investments consortium that completed their takeover at Leicester in August.
"I am both delighted and honoured to be named as Chairman of Leicester City," added Vichai on the club's website.
"Leicester City is a proud club, with a rich heritage. The primary reason for investing in Leicester City was not only because of my passion for football, but also my strong desire to revive and return the club to the Premier League.
"Leicester City has a history of playing Premier League football and it is time for a new chapter to be created."
The Foxes are managed by Sven-Goran Eriksson and are currently eighth in the Championship, four points adrift of the top six.
Source: BBC Sport