Mr Supachai made the announcement after today's meeting of Bhumjaithai.
Mr Chavarit, 76, submitted his resignation letter on Aug 29, citing his age as a reason and his wish to see new generation party members run the country's administration.
He will continue to serve as an MP and party's adviser.
Boonjong Wongtrairat, the party's secretary-general, is now acting party leader.
Mr Supachai expected the party to call a meeting to chose the new leader and a new party executive committee early next month.
Sources said the Friends of Newin faction in the party would nominate Anuthin Charnvirakul for the leadership and Saksayam Chidchob, a younger brother of party co-founder Newin Chidchob, for the secretary-general's post.
The other faction led by Somsak Thepsuthin had yet to name its nominees for the posts.