Reagan, then California Governor, made the comment in a 1971 telephone call with then President Richard Nixon, according to the former Director of Nixon's presidential library, which published it in The Atlantic.
Tim Naftali, who directed the Richard Nixon Presidential Library and Museum from 2007 to 2011, writes that an angry Reagan called Nixon in October 1971, the day after the UN had voted to recognise China and expel Taiwan.
In the call, Naftali says, Reagan a supporter of Taiwan is heard apparently referencing the way the Tanzanian delegation started dancing in the General Assembly when the UN took the vote to seat the delegation from Beijing instead of Taiwan.
Expressing his apparent frustration to the UN move, Reagan tells Nixon: "To see those... monkeys from those African countries - damn them, they're still uncomfortable wearing shoes!"
Nixon, who quit as President in 1974, can then be heard laughing.
Reagan wanted the US to withdraw from full participation, Naftali said.
The National Archives originally released the tape of the phone call in 2000 without the racist portion, but as a researcher, Naftali said, he requested in 2018 review of Nixon's conversations with Reagan.
The National Archives released the complete version of the recording online two weeks ago.
According to Naftali, Reagan called Nixon to press him to withdraw from the UN. But the President said Reagan's "complaints about Africans became the primary purpose of the call".
Naftali also said the President told his Secretary of State William Rogers that Reagan had described the Tanzanian delegation as "cannibals" that "weren't even wearing shoes".
Reagan publicly defended the apartheid states of Rhodesia and South Africa in the 1970s, and Naftali said the newly revealed recording "sheds new light" on this stance.
Reagan served as President from 1981 to 1989, at a time marked by the climax of the Cold War and the beginning of the end of Soviet communism. He died in 2004, aged 93, after a long battle with Alzheimer's.
The new audio comes weeks after President Donald Trump used racist language to attack four progressive Democratic congresswomen of colour, implying they weren't American and suggesting they "go back and help fix the totally broken and crime infested places from which they came".
The President faced swift backlash from both Democrats and Republicans, and the House voted to formally condemn Trump's racist language.
( With inputs from IANS )