Campbell is expected to be in Ames, Iowa, later Sunday, when an official announcement could be made.
The Toledo Blade earlier reported the move.
On Saturday, Toledo offered Campbell a contract that would have made him the highest-paid coach in the Mid-American Conference. He earned $495,000 with the school this past year.
"We think very highly of Matt Campbell and have made him a very generous offer to keep him as our head football coach," Toledo athletic director Mike O'Brien said Saturday.
Iowa State will pay a $200,000 buyout to bring Campbell aboard, sources said.
Campbell, who is 35-15 in four seasons at No. 24 Toledo after taking over for Tim Beckman late in 2011, will replace Paul Rhoads, whom Iowa State fired Monday.
Rhoads coached his final game with the Cyclones on Saturday, a 30-6 loss to West Virginia that left the team 3-9. Iowa State paid him $2.2 million this year.