The Prime Minister gave the Mendi bell to South African President Cyril Ramaphosa in a ceremony at Cape Town’s presidential office.
More than 600 men, the majority of whom were black South Africans, drowned after the SS Mendi was rammed by a British merchant ship.
The troop carrier was en route to the Western Front when the February 1917 incident occurred amid a pre-dawn fog.
Mrs May said: “I’m proud to be able to present the historic bell from the SS Mendi to President Ramaphosa and the people of South Africa.
“Six hundred and seven black troops from the South African Native Labour Corps who set sail from Cape Town just over a century ago sadly never reached their destination, and never served alongside many other Allied forces on the Western Front.
“Today is an important opportunity to commemorate this tragedy in our shared history and is yet another example of the close bonds, historical links and mutual respect which underpins the UK’s very close relationship with South Africa.”
The men were due to have helped build railways, trenches, camps and roads in support of the Allied war effort, according to Historic England.
The SS Mendi shipwreck lies just off the Isle of Wight.
The Mendi bell was found and restored last year after being lost from the shipwreck in the 1980s.