Lenzie and Edwards met in 2006 at Leeds University; Cameron was working in local record store Tribe Records and with Echo Location's Obi running local night Event Horizon, while Lenzie was DJing hip-hop and warming up Event Horizon for such acts as Rahzel and Grandmaster Flash. Once they had finished in Leeds, they relocated to London and became a three-piece with Edwards' school friend Ben Mauerhoff, being signed under DJ Fresh's Breakbeat Kaos. After a while, long distances took their toll – Edwards and Mauerhoff were based in Surrey, whereas Lenzie was based in Harpenden, Hertfordshire and they couldn't get three people into the Harpenden studio – and Mauerhoff left. In December 2008 they formed their own record label, Life Recordings (so called because, according to Lenzie, the industry demanded that it be their life). Its inaugural release was a VIP mix of their early Bingo Beats single "El Presidente".
Sigma have produced music for the Hospital Records label. In June 2009 they made the song "Paint It Black" for the compilation album Sick Music. Later that year came their second Life Recordings release "Nexus" / "Front to Back". In 2010, the duo released their two-part Stand Tall E.P. on the influential drum and bass label, Breakbeat Kaos. In December 2010, Sigma and DJ Fresh released the single "Lassitude" featuring Koko as the fifth and final single from Fresh's album Kryptonite. The song became one of their first charting singles as it peaked at number 98 on the UK Singles Chart and number 11 on the UK Dance Chart. After the release of their late-2011 Night & Day EPs on their label, Sigma began touring internationally in 2012. They toured the UK, Europe, Australasia and the USA. They were the supporting act for DJ Fresh on his first live UK tour. The tour included dates supporting fellow former Leeds student Christopher Mercer (a.k.a. Rusko).
The duo signed to 3 Beat Records in the summer of 2013. They had also remixed tracks for the likes of Ellie Goulding, Eric Prydz, Groove Armada, Skepta and Sway. Following their remix of the Stylo G single "Soundboy", they released their debut single with 3Beat, "Summer Calling", featuring Taylor Fowlis. Their second single with 3Beat, "Rudeboy", featuring Doctor, was released in December 2013. The song peaked at number 56 on the UK Singles Chart and number 12 on the UK Dance Chart. They released their third single with 3Beat, "Nobody to Love" (a rework of Kanye West's "Bound 2"), on 6 April 2014. It topped the UK Singles Chart upon release. To celebrate, they released a new song, "Divine", for free download on 16 April 2014. In July 2014, Sigma announced their single "Changing" co-written by Ella Eyre and featuring vocals from Paloma Faith; it was released on 14 September 2014 and became their second consecutive number one. They have also confirmed a collaboration with Shakka that will be released in the future.
Their third single "Higher" featuring Labrinth premiered on Annie Mac's Radio 1 show on 16 January 2015.
Sigma's fourth single "Glitterball" features vocals from Ella Henderson and is set for release on 24 July 2015. Their debut album Life is expected later in 2015.