“Rosalynn and I extend our condolences to the family of Queen Elizabeth II and the citizens of the United Kingdom,” said the statement issued by Mr Carter and former first lady, Rosalynn Carter.
“Her dignity, graciousness, and sense of duty have been an inspiration, and we join the millions around the world in mourning a remarkable leader.”
The Queen, who died on Thursday at the age of 96 after having served as monarch for 70 years, met 13 US presidents, including Mr Carter, who served from 1976 to 1980.
The Associated Press said the Queen hosted Mr Carter in May 1977 on his first overseas trip at a dinner for Nato leaders at Buckingham Palace. At one point, as Mr Carter stood with the queen and other guests, he noticed the arrival of the queen mother.
“Ever the Southern gentleman, Carter broke away, took her by the hand and escorted her to the assembled line of guests,” the AP said.
On Thursday Joe Biden issued his own tribute, saying that in a “world of constant change, she was a steadying presence and a source of comfort and pride for generations of Britons, including many who have never known their country without her”.
He said said her “history-making reign”, which spanned seven decades, “bore witness to an age of unprecedented human advancement and the forward march of human dignity”, and said she “led always with grace, an unwavering commitment to duty, and the incomparable power of her example”.
During her lifetime, the Queen met with all but one of the American presidents, Lyndon Johnson, since Harry Truman.
Former president Donald Trump also issued his respects, saying on Truth Social: “What a grand and beautiful lady she was. There was nobody like her!”
Barack and Michelle Obama also voiced a tribute, writing in a joint statement:
“Like so many of you, Michelle and I are grateful to have witnessed Her Majesty’s dedicated leadership, and we are awed by her legacy of tireless, dignified public service,” said the former president. “Michelle and I were lucky enough to come to know Her Majesty, and she meant a great deal to us. She welcomed us to the world stage with open arms and extraordinary generosity.”
George W Bush said in a statement: “Our world benefitted from her steady resolve, and we are grateful for her decades of service as sovereign.”
Former President Bill Clinton said in a statement that he and his wife, former secretary of State Hillary Clinton, were joining with people “all around the world” in giving thanks for her life.
He said: “Hillary and I mourn the passing of Her Majesty Queen Elizabeth II, and we join with people across the United Kingdom and the Commonwealth, and all around the world, in giving thanks for her extraordinary life.”