Snodgrass started his senior career with Livingston. He also had a loan spell at Stirling Albion before moving to England in 2008, joining Leeds United. He helped Leeds win promotion to the Championship in 2010. In February 2012, Snodgrass was appointed captain of Leeds, but he rejected a new contract offer and moved to Norwich City in July. He left Norwich after they were relegated in 2014 and moved to Hull City. On his league debut for Hull, Snodgrass suffered a serious knee injury that sidelined him for over a year. Hull were relegated in his absence, but Snodgrass helped them gain promotion via the playoffs in 2016. Snodgrass moved to West Ham United in January 2017.