The documents, released through Clinton's presidential library for the exhibit, also include talking points Clinton apparently used in his call with Nixon.
Nixon's trip to Russia was followed closely in the media, in part because Yeltsin froze the former president out of the Kremlin and took away bodyguards and a limousine the government had provided for him after Nixon held meetings with Yeltsin adversaries.
Yeltsin later backed off and urged Russian officials and parliament members to meet with Nixon.
In another glimpse into their relationship, a handwritten note will be on display from Nixon to Clinton that praises the former Arkansas governor's 1992 presidential campaign that helped put him in the White House. Nixon said the campaign was one of the best he had ever witnessed.
"The strongest steel must pass through the hottest fire. In enduring that ordeal you have demonstrated that you have the character to lead not just America but the forces of peace and freedom in the world," Nixon wrote.
Clinton in his younger days was no fan of Nixon — as a college student in the 1960s, he opposed escalation of the Vietnam War. And his wife, former Secretary of State Hillary Rodham Clinton, was a young lawyer advising a House committee when she helped draw up impeachment papers against Nixon.
But Clinton's views changed. He led the nation in paying tribute to Nixon at his funeral in California in April 1994, declaring, "May the day of judging President Nixon on anything less than his entire life and career come to a close."
He later told interviewer Larry King that he was deeply grateful for Nixon's counsel since he took office and wished he could call the former president for advice.
Clinton echoed that statement in the video tribute.
"After he died, I found myself wishing I could pick up the phone and ask President Nixon what he thought about this issue or that problem, particularly if it involved Russia. I appreciated his insight and advice and I'm glad he chose, at the end of his life, to share it with me," Clinton says.