He played his junior rugby league for the Townsville Brothers and attended Ignatius Park College, where he represented the Australian Schoolboys side in 2009.

[8] He spent the majority of the season in the Cowboys' NYC side, playing halfback in the Toyota Cup Grand Final against the New Zealand Warriors, which was lost 31–30 in extra time.

[11] From round 19 onward, Morgan cemented his halfback spot for the Cowboys after Ray Thompson suffered a shoulder injury.

[17] In 2014, Morgan shifted to fullback for the Cowboys after new signing Lachlan Coote tore his anterior cruciate ligament during the club's Auckland Nines tournament.

[18] Following an impressive season at fullback for the Cowboys, including two finals appearances, Morgan was selected on the interchange bench for the Prime Minister's XIII team which defeated Papua New Guinea 34–16 in Kokopo.

[26] In Game III of the series, Morgan scored a try with just his third touch of the football and set up two others in Queensland's 52–6 win over New South Wales.

After a great start to the season, on 6 May, Morgan was selected to make his international debut for Australia against New Zealand, where he played off the interchange bench in the 16–0 win at Hunter Stadium.

On 16 September, Morgan played his 100th NRL game, scoring the match winning try against the Brisbane Broncos in the club's 26–20 elimination semi-final victory.

With his halves partner Johnathan Thurston having injury issues/problems throughout the majority of the season; he spent time featuring at halfback, taking-on an extra responsible role in-steering and directing the team around the field.

[37] Playing at centre in the 3rd game (the decider), he produced a fine performance in QLD's 22–6 win over NSW at Suncorp Stadium.

[38] With Thurston still injured and out of the action; Morgan continued-on with his fine consistency performance at Halfback, leading into the NRL play-offs.

In week 1 of the Final Series, he guided the Cowboys to a tough narrow 15–14 win over the Cronulla Sharks at Allianz Stadium, kicking a field goal in extra-time .

[39][40][41] The following week, he then went-on playing a key role in the Cowboys' 24–16 win over the Parramatta Eels at ANZ Stadium.

Continuing to do his job for the Australia Kangaroos, he earned a spot at Five-eight for the 2017 Rugby League World Cup final against England.

On returning to the Cowboys it was revealed that Morgan was carrying a groin issue which was restricting his movement and required surgery at the end of the season.

On 8 March 2019, Morgan was named captain of the Cowboys, replacing Matt Scott and the recently retired Johnathan Thurston.

After playing the first two games of the season, Morgan underwent shoulder surgery during the NRL's 10-week shutdown, ruling him out for up to month ahead of the competition's return on 28 May.

[51] Following the Cowboys' Round 2 loss to the St George Illawarra Dragons, Morgan was indefinitely ruled out due to soreness to his surgically repaired shoulder.