The existing bridge was completed in 1929, and was named after a Governor-General of India, Lord Elgin (1862 – 1863). As this was the first bridge to be built across the river, the two roads leading to it were named North Bridge Road and South Bridge Road accordingly.
Elgin Bridge is believed to have existed at the place it is currently located as a footbridge as early as 1819, the year Sir Thomas Stamford Raffles landed on Singapore. The bridge served as a link between the Chinese community on the southern side of the Singapore River to the Indian merchants of High Street on the northern side, and was once the only place where one could walk across the Singapore River.
Elgin Bridge was rebuilt as a wooden drawbridge in 1822, and was officially named Presentment Bridge. It was also known as Jackson Bridge after Lieutenant Philip Jackson who built the bridge. As it was a very narrow bridge, it was also called Monkey Bridge, as people required some agility to get across it. Its narrowness limited the number of people crossing the bridge at any one time.
Elgin Bridge was later built as an iron bridge in 1862, and named after James Bruce, 8th Earl of Elgin who served as the Governor General of India during 1862 – 1863. The iron bridge was demolished in 1925 to make way for a new concrete bridge, but its name remained. Elgin Bridge was opened to traffic by the Governor of the Straits Settlements Sir Hugh Clifford on 30 May 1929.
Cavalari Rudolfo Nolli, an Italian sculptor, designed the elegant cast iron lamps on both sides of the bridge. His signature is inscribed beneath the lamps. Bronze plaques, each with a lion standing in front of a royal palm tree engraved on it, can also be found below the lamps.
Elgin Bridge is known as thih tiau kio in Hokkien, meaning "iron suspension bridge".
On 3 November 2008, the bridge was selected for conversation as part of the Urban Redevelopment Authority's expanded conservation programme.