The deal will run through 2018, and it is set to be voted on by the Arizona Board of Regents on Friday, Sep. 27.
The new terms mean Graham's salary will increase from $2.05 million to $2.3 million on July 1. From there, he will make $2.4 million in 2014, $2.5 million in 2015 and $2.6 million in 2016. His salary will increase by $50,000 annually from there.
There are other performance-based bonuses available to the coach.
Among the reasons cited for the contract extension by ASU are Graham's on-field success, where he guided the team to an 8-5 record in his first year, as well as the academic improvement the team has shown under his watch.
Other terms of the agreement are that the school can fire Graham without cause, though would have to pay his annual salary for the remainder of the contract term if it does. Conversely, if Graham elects to leave for another job, a $1.5 million buyout must be satisfied. That number drops to $1 million if at any point there are four or fewer years remaining on the contract.