If confirmed by the Senate, he would be the first career diplomat to serve in the post.
President-elect Biden, who assumes office on January 20th, has asked Congress to confirm his national security team as close to his inauguration as possible.
After a 33-year career at the State Department, Burns retired from the U.S. Foreign Service in 2014, having served under Republican and Democratic presidents. He holds the highest rank in the Foreign Service: career ambassador.
In a statement, Joe Biden said: "[Mr. Burns] shares my profound belief that intelligence must be apolitical and that the dedicated intelligence professionals serving our nation deserve our gratitude and respect."
Mr. Burns served as deputy secretary of state under former President Barack Obama, ambassador to Russia and Jordan, and assistant secretary of state for near eastern affairs.
Recently, he has written articles critical of the Trump administration's foreign policies and, last August, Burns warned about the risks of President Donald Trump not accepting an election defeat.
"If he loses, I doubt that he will suddenly embrace the traditional bipartisan commitment to effective transitions. At best, he'll be consumed by efforts to rationalize his defeat and paint the election as rigged; at worst, he'll seek to contest or undermine the result," Burns wrote in the Atlantic.
According to Biden, his national security and foreign policy priorities include plans to revive the Iran nuclear deal after President Trump withdrew the U.S. from it in 2018.
To date, Biden has also nominated General Lloyd Austin as his defense secretary, the 67-year-old who retired in 2016 and would become the first African-American to lead the Pentagon; Antony Blinken as his secretary of state, the 58-year-old whose work relationship with Mr. Biden goes back nearly 20 years; and Jake Sullivan as national security adviser, a former state department official and Hillary Clinton aide who also played a crucial role in negotiating the Iran nuclear deal.