The extension, which will run through the 2019 academic year, must be approved by the Arizona Board of Regents at its meetings June 5-6.
Murphy took over a program in disarray when he was hired for his first head-coaching job in 2012. The Lumberjacks lost their coach early the previous season and finished 1-15 in the Big Sky Conference.
NAU went 11-21 under Murphy in 2012-13 and he had the Lumberjacks in contention for a conference title until late last season, finishing 15-17 and 12-8 in the Big Sky.
His base salary of $185,400 will not change under the extension.
