Graeme made his debut for Dagenham & Redbridge in a League Two match, a 1–1 draw away at Barnet on 17 January 2009, when he came on as a substitute in the 89th minute for Jon Nurse.
During the 2009–10 season, he broke into the Daggers first team. On 17 April 2010, he scored his first ever football league goal – in the 95th minute, after he came on as a substitute for Josh Scott in the 2–1 home victory against Burton Albion.
On 18 November 2010, he was loaned to Hayes & Yeading United for one month. After the deal ran out, on 30 December, Graeme was signed by Newport County on another loan until the end of the season. In May 2011, Dagenham released Graeme at the end of his contract.
Graeme initially joined Conference South side Eastleigh, from Aldershot Town on loan, on 16 September 2011. The loan was initially for 1 month but, following impressive performances, the loan was extended by an extra month twice. Graeme was released by Aldershot and joined Eastleigh on a contract (until the end of the 2011/12 season) on 16 December 2011. This was short-lived, as due to new arrivals at the club, he lost his place in the starting line up and was eventually released from Eastleigh on 24 February 2012.
Graeme Montgomery signed for Boreham Wood on 5 March 2012 and scored 32 goals in 140 appearances. He joined the Saints on a 3-month loan deal in October 2015. In December 2015 he was recalled back from his loan and joined Hemel Hempstead Town. He then signed for the Saints at the beginning of December 2016. Graeme joined Hayes and Yeading United on loan at the end of February 2017.