Murray was born and grew up in Wodonga, Victoria, Australia. He was brought up in a non-golfing family but learned to take up the game at the age of 13. He had notable success as an amateur, including becoming the second-youngest men’s winner of the Victorian Amateur in 2013. He also added another victory in China, at the Aaron Baddeley International Junior against a strong international field. This win gave him a start at the 2014 Emirates Australian Open.
Murray won the 2015 Australian Master of the Amateurs by two strokes in a field which included future stars Bryson DeChambeau and Cameron Davis.
Murray won his first professional event at the 2018 Nexus Risk TSA Group WA Open while still having his amateur status. A final round of 69 saw him win by two strokes. He went on to turn professional a few weeks after this win.
Murray turned professional in November 2018. He won the 2019 New Zealand Open, becoming the third-fastest rookie to win on the Asian Tour. As the New Zealand Open was co-sanctioned by the Asian Tour and the PGA Tour of Australasia, it gave Murray full playing rights on both tours, until the end of the 2021 season.
His amazing performance in winning his first-ever professional title saw Zach lead from start to finish, and qualify for the Asian Tour, which he has played throughout the 2019 season.