The US president said he and wife Jill were keeping the Queen and her family “in our hearts” as he led international tributes to Philip.
“Over the course of his 99-year life, he saw our world change dramatically and repeatedly. From his service during World War II, to his 73 years alongside the Queen, and his entire life in the public eye — Prince Philip gladly dedicated himself to the people of the UK, the Commonwealth, and to his family,” Mr Biden said in a statement.
“The impact of his decades of devoted public service is evident in the worthy causes he lifted up as patron, in the environmental efforts he championed, in the members of the armed forces that he supported, in the young people he inspired, and so much more.
“His legacy will live on not only through his family, but in all the charitable endeavours he shaped.”
Other world leaders also offered their respects, with Irish President Michael D Higgins expressing his condolences to the Queen.
“On behalf of the people of Ireland, I wish to convey my condolences to Her Majesty Queen Elizabeth, her children, her extended family and the people of the United Kingdom,” he said in a statement.
He added: “For over 60 years, and as husband to Britain’s longest serving monarch, Prince Philip served the British people with an unfailing commitment and devotion to duty.”
“In the course of his long service he frequently brought an air of informality to otherwise formal occasions.
“His distinctive presence and unique sense of humour put participants at ease and always engaged those who encountered him.”
President Higgins added the Irish saying “Ar dheis De go raibh a anam dilis”, meaning may his holy soul be on the right side of God.
Barack Obama, who met the Queen and Philip when he visited as US president, tweeted: “Through his extraordinary example, His Royal Highness Prince Philip proved that true partnership has room for both ambition and selflessness — all in service of something greater.
“Our thoughts are with Her Majesty the Queen, the Royal Family, and the British people.”
Indian prime minister Narendra Modi recalled Philip’s “distinguished career in the military” and work “at the forefront of many community service initiatives”.
“May his soul rest in peace,” he added.
Along with Mr Modi, other leaders of Commonwealth nations marked the duke’s death.
Australian prime minister Scott Morrison tweeted that he “embodied a generation that we will never see again”.
Canada’s prime minister Justin Trudeau described Philip as a “man of great purpose and conviction” in a tribute posted on the social media platform.
“A man of great purpose and conviction, who was motivated by a sense of duty to others, Prince Philip contributed so much to the social fabric of our country – and the world,” he wrote.
“Prince Philip will be remembered as a decorated naval officer, a dedicated philanthropist, and a constant in the life of Queen Elizabeth II.”
The Kremlin said Russian President sent the Queen a message to convey his condolences.