Brown will also receive $500,000 as a special assistant to the president in a one-year contract, the unidentified school official said Wednesday.
His previous contract called for him to serve as special assistant until 2020, the Houston Chronicle reported Thursday.
The buyout will be paid in four yearly installments, and the $2.75 million amount equals what his previous contract called for if he was terminated before the end of 2013.
He earned $5.4 million as Texas coach in 2013.
Brown and the school negotiated the settlement after he announced in December he would step down after 16 seasons as Longhorns coach, the newspaper said.