Augusta National is home to the Masters, one of golf's most prestigious tournaments. In the past decade, it has come under attack for its all male membership.
Club chairman Billy Payne says consideration for new members is deliberate and private, but that both women are known and respected by Augusta members.
"These accomplished women share our passion for the game of golf and both are well known and respected by our membership," Payne said in a statement. "It will be a proud moment when we present Condoleezza and Darla their green jackets when the club opens this fall. This is a significant and positive time in our club's history and, on behalf of our membership, I wanted to take this opportunity to welcome them and all of our new members into the Augusta National family."
Both will receive the club's signature green jackets when Augusta opens for its new season in October. The move likely ends a debate that intensified back in 2002 when Martha Burk of the National Council of Women's Organizations urged the club to include women among its members.
On Monday, Burk said, "We won," and called it a milestone for women.
Rice said in statement that she has visited the club many times and looks forward to being part of Augusta.
"I have long admired the important role Augusta National has played in the traditions and history of golf. I also have an immense respect for the Masters Tournament and its commitment to grow the game of golf, particularly with youth, here in the United States and throughout the world."
Moore, who in the 1980s became the highest paid woman in the banking industry, said, "I am fortunate to have many friends who are members at Augusta National, so to be asked to join them as a member represents a very happy and important occasion in my life."
Augusta National, which opened in December 1932 and did not have a black member until 1990, is believed to have about 300 members. While the club had no female members, women were allowed to play the golf course as guests, including on the Sunday before the Masters week began in April.