This was the first time in more than two decades that the prize was awarded to two authors.
Announcing the joint winners, Peter Florence, chair of the judges, said that after five hours of discussion, the judges decided "two novels we cannot compromise on. They are both phenomenal books that will delight readers and will resonate for ages to come."
Gaby Wood, literary director of the Booker Prize Foundation, said the judges found it impossible to single out one winner from their shortlist of six and finally chose the twin winners.
Atwood's The Testaments is set more than 15 years after the events of her top selling book, The Handmaid's Tale, which is originally published in 1985.
This marks Atwood's second win, as the 79-year-old Canadian-born author won the 2000 Booker Prize for The Blind Assassin. She was also shortlisted for the prize in 1986, 1989, 1996 and 2003.
London-born Evaristo has become the first black female to win the prize. Her novel Girl, Woman, Other is described as a "fusion fiction," following the lives of 12 characters, most of whom are black, British and female.
The two winners will share a cheque for 50,000 pounds (about 62,890 U.S. dollars).
The Booker Prize had been jointly awarded twice before, but in 1993 the rules were changed so that only one author could win the prize. This is the first time since then that two authors have been announced as joint winners.