Greene attended and played hockey at Miami University for the RedHawks men's ice hockey team. He was signed as an undrafted NHL free agent by the New Jersey Devils in 2006 and was assigned to the team's American Hockey League affiliate, Lowell Devils, after New Jersey's training camp. He excelled at the AHL level, making the PlanetUSA All-Star Team. During his rookie professional season in 2006–07, Greene was called-up to the NHL for a short stint to replace the injured Johnny Oduya. Though Greene played well and showed considerable promise, he was reassigned to Lowell upon Oduya's return. Later in the season, he was again recalled when Colin White was injured. When the 2007 Stanley Cup playoffs began, the NHL salary cap no longer applied, allowing the Devils to add Greene to their permanent roster. With the return of injured defenseman Richard Matvichuk, it appeared as though Greene would sit. However, an injury to Colin White allowed Greene to remain on the roster. During this period, Greene played so well that, upon White's return, Oduya was scratched instead of Greene. On July 1, 2011, Greene signed a new four-year, $14 million contract with the Devils. On July 30, 2014, Greene signed a new five-year, $25 million contract with the Devils. Before the start of the 2015–16 season, Greene was named the Devils' captain, following the retirement of incumbent captain Bryce Salvador. The following season, Greene injured his hand in a game against the Carolina Hurricanes, resulting in him losing his streak of 350 consecutive NHL games played. His streak was the third-longest in Devils history, behind those of Travis Zajac and Ken Daneyko. At the conclusion of the season, Greene was the Devils' nominee for the Bill Masterton Memorial Trophy, awarded annually to the NHL player who best shows perseverance, sportsmanship and dedication to hockey. During the 2019–20 season, on February 16, 2020, Greene was traded to the New York Islanders in exchange for David Quenneville and a 2021 second-round pick. The move came following fourteen seasons with the club. The trade reunites Greene with Islanders general managerLou Lamoriello, who was general manager of the Devils in 2006 when Greene signed with the club.
Personal life
Greene and his wife Rachel have two children together. During the off-season, Greene returns to his hometown and organizes a hockey skills school called Andy Greene Hockey School. Greene's former high school, Trenton High School, officially retired his number in 2012.