Asofa-Solomona was born in Wellington, New Zealand, both of his parents having moved there from their native birthplace Samoa[3] He is the first cousin of Wests Tigers wing Ken Maumalo.

[14][15] In Round 20 against the St George Illawarra Dragons, he scored his first NRL career try in Melbourne's 22–4 win at McLean Park.

[19] 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.

[21] On 1 October 2017, in Melbourne's 2017 NRL Grand Final against the North Queensland Cowboys, Asofa-Solomona played off the interchange bench in the 34–6 victory.

[24] 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 part of the New Zealand national rugby league team tour of Denver, Colorado, in June 2018.

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.

[30][31] In the 2020 NRL Grand Final, Asofa-Solomona helped lead Melbourne to victory in their 20–26 win over the Minor Premiers Penrith.

[32] Asofa-Solomona played a total of 17 games for Melbourne in the 2021 NRL season as the club won 19 matches in a row and claimed the Minor Premiership.

[33] Asofa-Solomona played 23 games for Melbourne in the 2022 NRL season as the club finished 5th on the table and were eliminated in the first week of the finals by Canberra.

Following Melbourne's loss to Canterbury in round 2 of the 2023 NRL season, it was announced that Asofa-Solomona would miss six weeks with a high grade MCL injury.