Mr Kennedy's family say Mr Obama will be honoured because of his Obamacare expansion and climate change leadership - two policies Donald Trump has lambasted and is expected to change - and his diplomatic relations with Cuba.
“Humbled to be recognised by a family with a legacy of service,” said Mr Obama.
Mr Kennedy’s daughter Caroline Kennedy and her son Jack Schlossberg will hand over the trophy, which is a sterling silver lantern designed by Ms Kennedy’s husband, on 7 May at the John F. Kennedy Presidential Library and Museum in Boston.
"President Kennedy called on a new generation of Americans to give their talents to the service of the country," said Ms Kennedy in a statement.
"With exceptional dignity and courage, President Obama has carried that torch into our own time, providing young people of all backgrounds with an example they can emulate in their own lives."
The award is presented annually by the John F. Kennedy Library Foundation to public servants who have made courageous decisions of conscience without regard for personal or professional consequences.
It is named after Mr Kennedy's 1957 Pulitzer Prize-winning book Profiles in Courage.
The book tells the stories of eight US senators who risked their careers by taking principled stands for unpopular positions.
"Faced with unrelenting political opposition, President Obama has embodied the definition of courage that my grandfather cites in the opening lines of Profiles in Courage: grace under pressure," said Mr Schlossberg.
"Throughout his two terms in office, he represented all Americans with decency, integrity, and an unshakeable commitment to the greater good."
The foundation also said Mr Obama was being recognised for “enduring commitment to democratic ideals and elevating the standard of political courage in a new century”.
Last year's recipient, Mr Malloy, said: "From expanding access to affordable healthcare for millions of people, to reforming our criminal justice system, to restoring diplomatic ties with Cuba, to efforts to combat global warming - our nation and the world are forever changed for the better because of his work."
The award has been given out annually since 1990.
It sometimes awards groups of people, such as the “public servants of September 11” and the “people of Egypt” amid the Arab Spring.
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