He moved with his parents to their native Ireland at the age of four, where he spent most of his early years growing up in Carrick-on-Suir, the hometown of fellow cyclist Sean Kelly.

[4][5] Bennett was head-hunted by Vélo-Club La Pomme Marseille at 17, and joined them in the south of France, after completing his first year of third-level education at Waterford Institute of Technology (where he was embarking on an Honours Degree in Health and Exercise Studies).

In 2009, Bennett rode, for the first time, the Rás Tailteann with the Carrick Wheelers Dan Morrissey squad.

During the 2010 season, Bennett won the under-23 road race at the Irish National Cycling Championships in Sligo, aged 19.

The 2015 season began for Bennett at the Tour of Qatar, where he won the final stage, finishing in the Doha Corniche.

Bennett's Tour de France effort was hindered by a crash that resulted in broken fingers on his right hand, but he continued to finish the race last in the general classification – the lanterne rouge – and finishing in the top 10 on the final stage in Paris.

After recovering from his Tour injuries, Bennett went on to take a stage win at the Giro di Toscana, and won the points classification.

[17][18] Bennett became the sixth Irish cyclist to win a stage at the Tour de France, after Shay Elliott, Kelly, Stephen Roche, Martin Earley and Dan Martin, and the second, after Elliott, to win a stage in every Grand Tour.

[19][20] On 20 September, Bennett won his second stage of the Tour, becoming only the fifth cyclist to win the final stage of the Tour de France while wearing the green jersey, and the second Irish (and the second from the small town of Carrick-on-Suir[21]) cyclist to win the Green Jersey (after Kelly, who won it 4 times, in 1982, 1983, 1985, and 1989).

[30][31] In August 2021, Bennett was announced to be rejoining Bora–Hansgrohe on a two-year contract, along with his teammate Shane Archbold.