Gurung, who hails from Sikkim, played for ONGC from 2010-13. The 20-year-old defender will look to add depth to the Lajong backline.
Singh played for I-League champions Churchill Brothers from 2008-11 before joining Salgaocar SC.
"Shillong Lajong FC welcomes Vinay Singh and Robin Gurung to the home of the Reds," the club said in a statement.