Asofa-Solomona briefly trialled veganism, however found it did not work with his dietary requirements. Asofa-Solomona has, on multiple occasions, spoken of the influences his family has had on him throughout the years. In 2018, he stated that being able to provide for his family was one of the main perks of playing Rugby League for the Melbourne Storm. Asofa-Solomona has several tattoos, notably two Samoan designs - one on his right leg and one covering his right forearm. He has stated that the flowers in his leg design are a tribute to his sisters and the women in his life. Asofa-Solomona has two dogs. As of 2018, Asofa-Solomona is in a relationship with Georgia Wright.
In 2015, Asofa-Solomona graduated to the Storm's Queensland Cup team, Sunshine Coast Falcons. In Round 8 of the 2015 NRL season, he made his NRL debut for the Melbourne Storm against the Manly Warringah Sea Eagles, playing off the interchange bench in the Storms' 12-10 loss at AAMI Park. On 2 May, he again played for the Junior Kiwis against the Junior Kangaroos, playing at prop in the Kiwis' 22-20 loss at Cbus Super Stadium. In Round 20 against the St George Illawarra Dragons, he scored his first NRL career try in the Storm's 22-4 win at McLean Park. He finished off his debut year in the NRL having played in 12 matches and scoring 1 try.
On 1 February, Asofa-Solomona was named in the Storm's 2016 NRL Auckland Nines squad. Asofa-Solomona finished the 2016 NRL season with him playing in 15 matches for the Storm.
In February 2017, Asofa-Solomona was named in the Storm squad for the 2017 NRL Auckland Nines. In April 2017, Asofa-Solomona was called into the New Zealand Kiwis squad with a view to making his international debut against the Kangaroos but had to withdraw due to a hand injury. On 6 July 2017, Asofa-Solomona extended his contract with the Melbourne Storm to the end of the 2019 season. On 1 October 2017, in the Storm’s 2017 NRL Grand Final against the North Queensland Cowboys, Asofa-Solomona played off the interchange bench in the 34-6 victory. Asofa-Solomona finished his successful 2017 NRL season with him playing in 26 matches and scoring 4 tries for the Storm. On 5 October 2017, Asofa-Solomona was named in the New Zealand Kiwis 24-man squad for the 2017 Rugby League World Cup. On 28 October 2017, Asofa-Solomona made his international test debut for New Zealand against Samoa, where he played off the interchange bench and scored 1 try in the 38-8 win at Mt Smart Stadium.
Asofa-Solomona was awarded 2 Dally M points for his round one appearance in the victory over the Brisbane Broncos. He won a popular vote for tackle of the round for his hit on Matt Gillett. Round two saw Asofa-Solomona score his first try of the season. Asofa-Solomona played 27 games for Melbourne in the 2019 NRL season as the club finished as runaway minor premiers. Asofa-Solomona played in the club's preliminary final defeat against the Sydney Roosters at the Sydney Cricket Ground.
Controversy
In October 2019, Asofa-Solomona was involved in an ugly brawl whilst on holiday in Bali. The NRL later fined Asofa-Solomona $15,000 and handed him a three-match test ban for New Zealand which saw him miss both matches against Great Britain and Australia. Asofa-Solomona claimed he reacted violently after it was alleged his Melbourne teammate Suliasi Vunivalu was king hit by an unidentified male.
