The British actress, 48, and director, 56, ‘separated amicably earlier this year and have continued to be friends and co-parent their children,’ Ms Bonham-Harter’s rep told People.
‘We would ask that you respect their privacy and that of their children during this time.’
The two — who were never married — have an 11-year-old son, Billy, and seven-year-old daughter, Nell, together.
The exact date of their split has not been announced, but in June, Bonham Carter told People that Burton represented the word “love”.
A spokesperson for Bonham Carter last year dismissed as “absolute nonsense” claims that Burton had cheated on her.
Bonham Carter starring in Sweeney Todd, in which Burton directed her.
That claim followed Burton being pictured with a mystery blonde woman at a cinema in north London.
They first met in 2001 when he directed her in Planet Of The Apes.
They also worked together on Charlie And The Chocolate Factory, Sweeney Todd: The Demon Barber of Fleet Street, Alice In Wonderland and Dark Shadows.
Burton and Bonham Carter on the red carpet for the 85th Annual Academy Awards last year. (Photo: Valerie Macon/AFP/Getty Images)
The Bonham Carter-Burtons lived in a series of three adjacent houses in London; one home was decorated according to each of the couple’s taste, while the third home was for their nanny.
The couple has not confirmed whether they will continue to live in those houses following their split, or where their children are now residing.