The extension must be approved by the Arizona Board of Regents when it meets June 5-6.
Rodriguez has led the Wildcats to a pair of 8-5 seasons and two bowl wins since arriving in Tucson.
Rodriguez will receive $500,000 for peripheral duties like radio and TV appearances, and has numerous performance incentives, including $1 million for a national title and $300,000 for a Pac-12 championship.
Arizona athletic director Greg Byrne also has agreed to a one-year contract extension through 2019 that will raise his base salary to $725,000 by the end of the deal.
In addition, a university donor created a retention plan that would keep Rodriguez, Byrne and men's head basketball coach Sean Miller in Tucson for the next eight years.
Under the plan, they would receive part of a 500,000-unit donation of a Master Limited Partnership to the University of Arizona Foundation if they are still employed by the school after eight years. Rodriguez would receive 175,000 units and Byrne 100,000 under the proposal.
Both would receive a prorated amount from the unit value through the first four years.
The MLP units were valued at $35.36 each as of May 12 for a total donation of $17.68 million.
• Arizona's Miller agrees to extension