Born in Trinidad to Indo-Trinidadian parents, Singh moved to India in 1984 and studied at Madras University during which he played club and college-level cricket. He helped Tamil Nadu win the Ranji Trophy in 1988, and was one of the season's most consistent players. He gave up his Trinidad and Tobago passport so he could become an Indian citizen and play for India's national cricket team.
Singh was born in Princes Town, Trinidad and Tobago, to Ramnarine and Savitri Singh on September 14, 1963, and is of Indian descent. At the age of 19, Singh moved to Madras, India, where he earned a master's degree in economics at the University of Madras while beginning his cricket career. He currently resides in Chennai (Madras), India, with his wife Sujata and son Dhananjay, although his parents and siblings still live in Trinidad and Tobago.
While in Trinidad, Singh captained the Trinidad youth cricket team in regional tournaments from 1982 to 1983. He represented the senior Trinidad cricket team in two one-day matches in 1983, during which he played alongside Phil Simmons, David Williams, Larry Gomes, Gus Logie, Rangy Nanan, Sheldon Gomes, and Richard Gabriel.
Singh started his first-class career for Tamil Nadu during the 1985–86 season. During his nearly two decade career, he was a genuine all-rounder for his club, making more than 6,000 runs and taking 172 wickets with his medium-fast bowling.
Singh made his debut for the Indian national cricket team in a One Day International against the West Indies cricket team on 11 March 1989. He played two one-day Internationals, coming in to bat at number 7 both times in futile situations. The Indian team dropped Singh after the series, and he played in domestic and overseas leagues for the next seven years, after which he secured a regular place on the Indian cricket team. Singh was recalled for the Titan Cup tournament in 1996. He remained a regular player in the One Day Internationals until 2001. Singh was known for his middle-to-lower order batting, medium-pace bowling, and his ground fielding skills. He was also known for his batting in closing overs (usually along with Ajay Jadeja), which made him an integral player during the 1999 Cricket World Cup. Throughout his career, Singh was considered a better fit for One Day matches.
Singh began coaching soon after his retirement. His first coaching position was with the Indian under-19 cricket team. In 2004, he began coaching the Hong Kong national cricket team, helping it qualify for the 2004 Asia Cup. In 2006, Singh was appointed coach of the India A cricket team, where he coached cricketers such as Gautam Gambhir and Robin Uthappa. Several cricketers whom Singh coached went on to play for the Indian national team. Singh was named the Indian national team fielding coach in 2007 and 2008 and was appointed the first head coach of the Deccan Chargers franchise in the Indian Premier League.
Singh remained the fielding coach for the Indian national cricket team until October 2009 and is (as of 2017) the batting coach of the Mumbai Indians, an Indian Premier League team. He helped the Mumbai Indians occupy the runner-up position during the 2010 IPL season and win the 2013 IPL season, the [[2015 Indian Premier League|2015 IPL season] 2017 Indian Premier League, the 2013 Champions League Twenty20, and the 2011 Champions League Twenty20.
Singh coached the Khulna Division cricket team in the Bangladesh Premier League, where he helped Dwayne Smith and Andre Russell further their cricket skills. In 2012, the Uva cricket team, under Singh's coaching, won the Sri Lanka Premier League tournament.
He is also the coach of the Barbados Tridents. Since its inception, the Tridents have won once, and have played two finals and a semifinal.
Singh has also helped coach the senior and junior USA cricket teams. In 2011, Singh coached the United States women's cricket team at the World Cup Qualifier Tournament in Bangladesh.