From the northern suburbs of Perth, Tye played second XI cricket in England for Somerset, Durham and Northamptonshire before making his list A debut in the 2013–14 Ryobi One-Day Cup aged 26.[2] He took the second most wickets in the tournament and returned the best single innings bowling figures of 5 wickets for 46 runs against Tasmania.[3][4]
He was seen as a breakout player in BBL|04, with Australian T20 captain Aaron Finch labelling him as the 'find of the tournament'. He enjoyed success with the team, and was a focal contributor to Perth's second successive Big Bash League title.
In January 2018, Tye was bought by Kings XI Punjab in the 2018 IPL auction.[11] During the tournament, Tye broke a record. On 16 May 2018, against the Mumbai Indians when he picked up the figures of 4–16, he went on to become the first ever player to take three 4 wicket-haul in a single season of the IPL.[12] Tye then went on to win the Purple Cap for the 2018 IPL season for taking the most wickets (24) during the season.[13] For his excellent performances in the 2018 IPL season, he was named in ESPNcricinfo’s and Cricbuzz’s 2018 IPL team of the tournament.[14][15]
On 23 March 2022, Tye was signed as replacement for the injured Mark Wood by the Lucknow Super Giants. In the 2022 season, he played only 3 matches taking 2 wickets. He was released by the Lucknow Super Giants ahead of the Indian Premier League 2023 Auction.
In the 2023 Auction, he had kept a base price of 1 cr. but was unsold.
In April 2018, he was awarded a national contract by Cricket Australia for the 2018–19 season.[22][23] He went on to become the leading wicket taker in T20IS in 2018 with 31 wickets.[24] On 16 July 2020, Tye was named in a 26-man preliminary squad of players to begin training ahead of a possible tour to England following the COVID-19 pandemic.[25][26] On 14 August 2020, Cricket Australia confirmed that the fixtures would be taking place, with Tye included in the touring party.[27][28] In November 2020, Tye replaced Kane Richardson in the Australian squad for T20I and ODI matches against India.[29]