An inaugural Giant taken at pick 11 in the 2011 draft, Greene was appointed sole captain by Adam Kingsley ahead of 2023 and answered with a career-best 66 majors, a preliminary final, the Kevin Sheedy Medal and a third All-Australian selection, this time as captain of the side. In 2025 he became the second player to reach 250 matches for Greater Western Sydney and kicked his 400th AFL major. He has played 282 AFL games and kicked 450 goals.