Simpson spent time in Thailand with Buriram United, winning the 2014 Kor Royal Cup before returning to England with Leyton Orient.

He later played two years with Philadelphia Union of Major League Soccer, before returning to England and rejoining Orient.

On 19 February 2007, he made history by becoming the first player ever to score a hat-trick at the Emirates Stadium, for Arsenal's under-18 team in an FA Youth Cup match against Cardiff City, in a 3–2 win.

"[9] Simpson made his Arsenal first team debut in a 6–0 win over Sheffield United in the third round of the League Cup on 23 September 2008, coming on as a substitute for Nicklas Bendtner in the 71st minute.

[11] The next day, he made his first team debut in a 2–1 League One defeat to Huddersfield Town at The New Den, replacing Danny Spiller for the final eight minutes.

[17] Simpson scored eight goals in 44 appearances for Millwall and won the PFA Fans' League One player of the year award for 2008.

[20] He made his Albion debut on 3 January 2009, coming on as a half-time substitute for Robert Koren in a 1–1 draw with Peterborough United at The Hawthorns in the FA Cup third round.

[23] After making seventeen appearances and scoring two times in all competitions, the club were relegated back to the Championship after one season in the Premier League.

On 19 August 2010, Simpson signed a three-year contract with Championship team Hull City for a fee of £1 million including add-ons.

[33][34] It came after when Simpson can leave Arsenal, prompting interests from clubs, such as, Queens Park Rangers, Fulham and Millwall.

[40] After spending over a month as an unused substitute, he made his return coming on as a replacement for Tijani Belaid, and scoring his fifth goal of the season in the 1–1 away draw at Ipswich Town on 19 February 2011.

[43] As a result, Simpson signed again for Millwall on loan, on transfer deadline day, 31 August 2011, remaining with them until the new year.

[44] He made his Millwall debut for the second time on 11 September 2011, where he played 72 minutes before being substituted, in a 3–0 loss against Birmingham City.

[48] After making sixteen appearances and scoring four times in the first half of the season, Simpson returned to his parent club.

[50] In the 2012–13 season, new Manager Steve Bruce was impressed with Simpson's performance after scoring four goals in two friendly matches, including a hat-trick, with a 5–0 win over Winterton Rangers.

[57] After scoring against Wolverhampton Wanderers on 6 November 2012, Simpson played a vital two weeks later when he set up two goals, in a 3–2 win over Birmingham City.

[85] By the end of 2015, Simpson scored nine goals in ten matches against York City (twice),[86] Plymouth Argyle,[87] Wimbledon,[88] Mansfield Town,[89] Portsmouth,[90] Bristol Rovers[91] and Stevenage (twice).

[96] At the end of the 2015–16 season, Simpson went on to make forty-eight appearances and scoring twenty-five goals in all competitions, finishing as the second's top-scorer behind Matty Taylor.

[103] After returning to the first team from injury, Simpson suffered a goal drought since the start of the season and it wasn't until on 12 November 2016 when he scored a brace, in a 3–0 win over Colchester United.

[114] In November 2022, Simpson returned to England when he joined National League South club Welling United.

[116] However in March 2023, Welling United were deducted 1 point in the National League South due to the club not having international clearance for him.