Moore was born in Liverpool, England. He holds a bachelor's degree from Keele University, England, and a master's degree from California State University. He worked for Patrick USA, the US subsidiary of a French sportswear company, and then at Reebok for almost two decades. He also was a physical education teacher for a number of years.
After Reebok, Moore was hired by Bernie Stolar to work at Sega. Despite his son owning a Sega Saturn, Moore knew little about video games. However, Moore quickly rose to prominence at Sega, being a big figure in the company's North American operations during the Dreamcast era. Moore played a pivotal acting role in the company's decision to change its business strategy to become a platform-agnostic software publisher. At the time of leaving, Moore was president and COO of Sega of America.
Moore has been proud of the success of the Dreamcast game console and the satisfaction that owners still express today; including fans of the Shenmue game franchise, which Moore describes as the most vocal fan base during his career at Sega. Moore disclosed to GamingSteve.com that at a security checkpoint at Chicago O'Hare International Airport, a TSA security agent said "I don't need to see your passport. You're the asshole that gave away Shenmue to Xbox". Many blame Moore for using Sega as a career ladder while misusing Sega. However, Moore has admitted to being responsible for the discontinuation of the Dreamcast. He said:
"We had a tremendous 18 months. Dreamcast was on fire – we really thought that we could do it. But then we had a target from Japan that said we had to make x hundreds of millions of dollars by the holiday season and shift x millions of units of hardware, otherwise we just couldn't sustain the business. So on January 31st, 2001, we said Sega is leaving hardware. We were selling 50,000 units a day, then 60,000, then 100,000, but it was just not going to be enough to get the critical mass to take on the launch of PS2. Somehow I got to make that call, not the Japanese. I had to fire a lot of people; it was not a pleasant day."
During his stint at Sega, Moore also portrayed a zombie in the film adaptation of House of the Dead along with producer of the original game Rikiya Nakagawa. Both are credited at the end of the film under "Special Thanks".
In 2012, a history book titled Service Games: Rise and Fall of Sega covered Moore's entire career at SEGA.
In 2003, Microsoft hired Moore to help the Xbox compete with other next generation consoles. Microsoft CEO Steve Ballmer had been frustrated by the low market share of Xbox (then stalled at 23% in the United States).
At Microsoft, Moore gained notoriety for displaying tattoos of Halo 2 and Grand Theft Auto IV that he used when announcing the respective games (the former was used to announce Halo 2's release date of November 9, 2004, while the latter was used to announce Grand Theft Auto IV). Some sources claim that the Halo 2 tattoo was not permanent and others have reported that Moore still has it.
Moore also reportedly endorsed the Wii console as an alternative over the PlayStation 3, claiming that for the price of one PlayStation 3 (US$599 at the time), the consumer can buy both the Xbox 360 and Wii.
On 17 July 2007, Electronic Arts announced that Peter Moore would be leaving Microsoft to head the sports division at Electronic Arts. Moore reportedly wanted to move back to the San Francisco Bay area to live with his family, which was possible with EA. His position as Vice-President of Interactive Entertainment Business at Microsoft was filled by Don Mattrick (who later also left Microsoft to join Zynga as CEO).
Moore was parodied in an episode of South Park, Season 15's Crack Baby Athletic Association, focusing on the NCAA's relationship with Electronic Arts. On 4 August 2011, Moore was promoted from EA Sports President to the role of chief operating officer in a structure reshuffle. An image of him can be seen in Criterion's 2012 video game Need for Speed: Most Wanted on a wanted billboard.
On December 10, 2015, Moore was appointed as the "Chief Competition Officer" of EA's newly formed competitive gaming division.
Moore left EA and was announced as the new CEO of the Liverpool Football Club on February 27, 2017. Moore took up his new role on 1 June 2017 and reported directly to the club’s owners, Fenway Sports Group.