The name change will be made when the competition changes format next year and the prize money has increased to the equivalent of SEK 105 million, the International Tennis Federation writes in a press release.
At the same time, the competition changes its name to the Billie Jean King Cup.
76-year-old Billie Jean King won twelve grand slam titles in singles during his career.
She was also a leading figure in the fight for equality in tennis.
"The new name is a fitting tribute to everything she has accomplished and gives her a legacy that will live on for a long time and inspire new generations of players and fans," said David Haggerty, president of the International Tennis Federation, in a statement on the federation's website.