"The son-of-a-bitch, didn't you think he was about the worst candidate?" Nixon said then.
This latest batch of tapes is now available on-line from the Nixon library.
McGovern, in Washington celebrating his 85th birthday with old friends and supporters, heard for the first time what he was never intended to hear.
"I have no malice towards him, I didn't then and I don't today," McGovern told CBS News correspondent Bill Plante.
The raw material of history is sometimes very raw.
"You know, this fellow to the last was a prick," Nixon said.
National security advisor Henry Kissinger was quick to agree.
"He was ungenerous, he was petulant, unworthy," he said.
The big issue in 1972 was ending the Vietnam War. Nixon tells New York Governor Nelson Rockefeller that he's on the verge of a peace deal.
"We got a wire from the North Vietnamese, they've agreed to negotiate without conditions in one week," Nixon said. "It's all done."
But it wasn't. The deal fell apart. And McGovern remains convinced that the race he ran helped end the war.
"We lost that campaign, Bill, but I'm proud of it," he said. "It wasn't a mistake to label that war for what it was."
Taking congratulatory calls the day after the election, Nixon is heard still complaining about McGovern.
"Wasn't that fellow unbelievably irresponsible in the last two days?" Nixon said.
"I do think it's kind of sad that the president of the United States in the moment of his greatest triumph was so angry," McGovern said after listening to the tape.
And the way things turned out, says McGovern, "He'd have been better off if I had won," he said. "Because he wouldn't have been thrown out of office in disgrace."