Murphy started his youth career with Newcastle United before joining Norwich City’s youth system in 2011. In August 2013, he made his professional debut for Norwich City in a League Cup match against Crawley Town.

He went on to make his league debut for the club in November 2013 and appeared in 18 games during the 2013-14 season.

Murphy signed for Newcastle United on 19 July 2017. He has a twin brother Josh who is also a professional footballer.