He would be the school's fourth head coach in 13 months.
The newspaper said Chryst, 46, a leading candidate for the job, would be introduced to the media at 3 p.m. Thursday.
Though the terms of his contract at Pittsburgh were not immediately available, the Tribune-Review said, he received a base salary of $405,000 this past season. It was his seventh season as offensive coordinator at Wisconsin.
Chryst could not immediately be reached for comment, the newspaper said.
He takes over after former Coach Todd Graham resigned to take the head coaching job at Arizona State Dec. 13. Others being considered for the Pitt job were Florida International Coach Mario Cristobal and Ohio State interim Coach Luke Fickell, the newspaper said.
Pitt Athletic Director Steve Pederson actually had interviewed Chryst for the coaching job before hiring Graham in January. Graham was signed to a five-year contract worth nearly $2 million annually, including incentives, the newspaper said. His departure from Pitt stunned university officials. Arizona State officials said there was a $1 million buyout for Graham's contract.
The Tribune-Review said the Pitt head football job has been in upheaval since last December, when Dave Wannstedt was forced to resign. Pitt first hired Mike Haywood from Miami (Ohio), then fired him two weeks later after Haywood was charged with domestic battery.
Pitt then hired Graham, who was Tulsa's head coach.