The sculpture, titled The Campbell Sisters Dancing a Waltz, has been subject to a temporary export bar since 2014.
A total of £523,800 was jointly raised to keep the sculpture in the United Kingdom.
Of that, £275,000 came from the National Heritage Memorial Fund, £98,800 from the Art Fund and the remainder from the Victoria and Albert Museum and NGS contributions.
The Campbell Sisters will be shown for the first time this week at London’s V&A, and will remain on display in the Dorothy & Michael Hintze Sculpture Gallery until 20 November.
After that it will be on show at Edinburgh’s Scottish National Gallery, where it was previously on long-term loan.
Italian-born Bartolini, trained in Paris and Florence, is recognised as one of the leading European sculptors of his era.
“We are excited that we have the opportunity to display The Campbell Sisters Dancing a Waltz at the V&A,” said Beth McKillop, deputy director and director of collections at the V&A, “Bartolini’s sculpture is a delightful work and an outstanding addition to the national collection of sculpture housed at the Museum.”
Director of the Scottish National Gallery, Michael Clarke said he was ‘thrilled’ the masterpiece, which features two Scottish sisters, would be returning.
“For nearly two centuries it was on view in Inveraray Castle, Argyll, and most recently in the Scottish National Gallery in Edinburgh,” he said. “Now it will return to the Gallery, where it links beautifully to many other great works of art in the national collection.”
Culture Minister Ed Vaizey said: “This vibrant work by Bartolini provides a fascinating insight into the cultural history of the British presence in Florence. I am delighted that the V&A and National Galleries Scotland have come together to save the sculpture for the entire country to enjoy for years to come.”