A source close to Barnett told the Denver Post the coach reached a $3 million settlement with CU to offer his resignation.
"In the last 24 hours, (CU athletic director) Mike (Bohn) made a decision to change football coaches at the University of Colorado," Barnett said.
"I respect that decision," Barnett added. "I don't like that decision."
The new allegations, contained in an unsigned latter, went to CU President Hank Brown, who requested an investigation. A private investigator who found the letter said he believed it came from "a former employee of the athletic department."
The letter included assertions that Barnett attempted to influence the sworn testimony of subordinates plus charges of NCAA violations and financial improprieties, the Rocky Mountain News said Thursday.
Among the alleged NCAA violations is a charge that football players were tipped off in advance of what were supposed to be random drug tests.
The dismissal follows three high-profile losses and the aftermath of a recruiting scandal that spawned numerous investigations, a grand jury probe, federal lawsuits and news reports that tarnished the school's reputation.
Barnett said Bohn offered him the chance to coach CU against Clemson in the Dec. 27 Champs Sports Bowl, but he said he probably would not do so.
Barnett had a 49-38 record in seven seasons at Colorado, and his team won four of the past five Big 12 North division titles.