Green was born in the United Kingdom and grew up in Australia. He began his competitive career in 1981 with Newman Racing in the Can-Am series, winning five races and six pole positions across the 1981 and 1982 seasons. He then joined the Champ Car team Forsythe Racing in 1983, spending the following decade building his reputation within the CART series.
In 1994 Green joined his brother Barry's organisation, Team Green, as team manager. With Jacques Villeneuve driving, Team Green won both the 1995 Indianapolis 500 and the CART PPG IndyCar World Series Cup. The team's identity evolved through the late 1990s: it raced as the Brahma Sports Team in 1996 with Raul Boesel, then became Team KOOL Green from 1997 when KOOL cigarettes took over as principal sponsor with Parker Johnstone. A two-car effort launched in 1998 with Paul Tracy and Dario Franchitti.
In 2001 Michael Andretti joined the organisation with a separate effort entered as Team Motorola, run under Green's management. In July 2002, Andretti purchased a controlling stake and the combined operation was renamed Andretti Green Racing. Moving from Champ Car to the IRL IndyCar Series, the team won the IndyCar Series championship in 2004, 2005, and 2007, and claimed the Indianapolis 500 in 2005 and 2007. Green and fellow co-owner Kevin Savoree departed Andretti Green Racing in September 2009.
Green co-founded Green Savoree Racing Promotions in 2009 with Kevin Savoree, creating an Indianapolis-based company focused on owning, operating, and promoting auto-racing events across North America. GSRP launched IndyCar's street race in St. Petersburg, Florida — which the company describes as the first IndyCar street race — in 2005, and has since promoted the event annually as the Firestone Grand Prix of St. Petersburg. The company also promotes the Grand Prix of Portland at Portland International Raceway and the Honda Indy Toronto, which from 2026 moves to Markham, Ontario, as the Ontario Honda Dealers Indy at Markham.
On 2 March 2011, GSRP purchased the Mid-Ohio Sports Car Course in Lexington, Ohio, adding the celebrated road course and its driving school to their portfolio. Through these properties, Green and Savoree have hosted IndyCar, NASCAR, IMSA, and other racing series.
The Canadian Motorsport Hall of Fame named Green and Savoree as International Inductees for its Class of 2025, citing their role in preserving IndyCar racing in Canada. After the final CART/Champ Car event in Toronto in 2007 left the race without a future, Green and Savoree acquired its promotional assets and restored the event to the IndyCar calendar in 2009. CMHF Board Chair Peter Lockhart noted that their work had provided "long-term stability for the Toronto race" and secured Canada's place on the IndyCar calendar. Green and Savoree were formally inducted at the Induction Gala on 21 February 2026 at the John Bassett Theatre in Toronto during the Canadian International Auto Show.
Green is based in St. Petersburg, Florida.