Forward / winger Joshua Murphy was featured as the Academy profile in the Norwich City matchday programme with Bristol City on 14th March 2011. He joined Norwich as an Under-12 in 2006. Previously he had played for a boys team, Pitshanger, from which he won trials with Fulham and Spurs. He spent a while with Spurs and then with QPR before joining Norwich.

.On 31st March 2011, it was announced that he and eight others, including twin brother Jacob, would join Norwich's Academy in the summer of 2011. Academy manager Ricky Martin said: “I would like to wish all nine boys the best of luck and hope they enjoy long and successful careers at Norwich City.”

He was on the bench for the Capital One Cup clash with Doncaster on 26th September 2012.

Along with twin brother Jacob, Josh made his debut for England's Under-18s in October 2012 against Italy, coming on as substitutes. On 13th November, the Twins made their England Under-19 debuts playing in a 1-0 win over Finland, with Jacob starting and Joshua coming on as substitute.

Jacob and Josh signed professional contracts with Norwich until the end of the 2014/15 season on 4th January 2013. Norwich City manager Chris Hughton told the club’s official website: “I’m absolutely delighted to have secured the futures of Jacob and Josh at Norwich City. They’ve shown that they have great potential and have certainly earned these contracts with their hard work. We only give out contracts when we feel that they have been earned, and this is certainly the case with Jacob and Josh.They’re both exciting players and more importantly they are good lads who we’re pleased to have at this football club.”

Josh said: “It’s amazing. It’s the best feeling. Jacob and I have worked so hard for this and we’ve been rewarded with these contracts. Now we just want to kick on towards the first team.So much work has gone into getting us here you wouldn’t believe – loads of extra training after our normal training sessions, and whenever we get time off we just practice, practice, and practice.Chris Hughton has helped us a lot. He really likes young players and he has given us the opportunity to be in and around his team so we’re just thankful for everything.”

Josh played in both FA Youth Cup semi-final matches against Notts Forest which the Canaries won to progess to the FA Youth Cup final. He also played in both legs of the final which the Canaries won 1-0 and 3-2 against Chelsea to secure victory in the FA Youth Cup for the first time in 30 years.

He joined the Norwich City Under-21 Development Squad and travelled with the first team to the USA in the summer of 2013. He made his Norwich debut, coming on as substitute in the Capital One Cup away game at Watford on 24th September 2013, scoring Norwich's first goal and provoking a comeback from 2-0 down to win 3-2. His first league appearance came in the 7-0 mauling at Manchester City on 2nd November 2013. He made up for this by scoring once and providing two assists as England Under-19s beat Hungary 4-1 on 14th November 2013. His performance was described in the match report on the FA’s official website as “outstanding”. He was replaced in the 63rd minute by his twin brother Jacob.

He made 13 appearances, scoring once in the 2013/14 season in which Norwich were relegated from the Premier League.

Josh was loaned to Wigan for a month on 16th March 2015. He had made 16 appearances for Norwich in the 2014/15 season scoring three goals. Wigan manager Malky Mackay said "Josh will be another great addition to what is still a small squad here. He is a great young talent."

On 21st August 2015, he joined MK Dons on a season long loan. He scored seven goals in 46 appearances and was named Player of the Season.

Josh made 32 appearances for Norwich in 2016/17 scoring five goals.

Josh made his 100th appearance for Norwich in the 3-2 win over Reading on 17th March 2018.

After scoring 11 goals in 47 appearances in 2017/18, he was signed by Premier League newboys Cardiff for a fee believed to be about £11m on 12th June 2018. "Josh is a player I've watched for a number of years now and he's always excited me when he runs with the ball," said Cardiff boss Neil Warnock who described him as his number one target.

Josh made 29 appearances for Cardiff in his first season in South Wales, scoring three goals but it was not enough as Cardiff were relegated to the Championship on 4th May 2019.

There were reports in early February 2020 that Celtic had made enquiries about Murphy during the January 2020 transfer window with The Sun reporting that Celtic tried to sign him on Transfer Deadline Day and that Murphy is on their shortlist for their Summer 2020 transfer targets.

Having fallen out of favour with Cardiff manager Neil Harris and not having played since November 2020, Josh was linked on 19th January 2021 with a loan switch with Championship trio Notts Forest, Derby County and Sheffield Wednesday all reported to be keen.

On 1st September 2021 it was reported that Murphy had joined Preston on a season-long loan. 26-year-old Murphy worked with North End head coach Frankie McAvoy during their time with Norwich City. Murphy had played 99 times for Cardiff.

Murphy was out of contract with Cardiff at the end of the 2021/22 season. He trialled with Oxford United in July 2022 playing for them against AFC Wimbledon on 23rd July 2022. He then signed a two year deal with them on 26th July 2022. He said "I want to excite fans and get them off of their seats. My style is direct, I want to go at opponents and get lots of shots and crosses in to win games." He played under Oxford manager Karl Robinson at MK Dons.