"At the end of what will be my last campaign, I want to say to Minnesota, you always treated me well, you always listened to me," the 74-year-old former vice president told supporters.
Coleman's victory over one of Minnesota's revered statesmen was part of a national Republican tide, and a symbol of strength for President Bush. Coleman was the White House's chosen candidate, and Mr. Bush and Vice President Dick Cheney visited the state several times on his behalf.
With 98 percent of precincts reporting, Coleman had 1.02 million votes, or 50 percent, to Mondale's 974,174, or 48 percent. Three independents split the rest.
"It appears that this election has been decided and a few minutes ago I called Sen.-elect Coleman to congratulate him on his success and wish him and Laurie the best in his new assignment," Mondale told supporters. "I told him what I really believe, that the U.S. Senate is the best job in America, and I think he will love it."
Mondale called his brief campaign "one of the most unbelievable moments in Minnesota history, perhaps in modern American history."
Coleman had worked frantically for the victory, ending his two-year bid for office with a 3,000-mile travel blitz in the last days. On the final night alone, he campaigned in twice as many cities as Mondale did in his entire brief campaign.
Late Tuesday, Coleman talked of a "Republican wave" sweeping the party to victories around the country.
"The wave is moving from east to west and we're waiting for it to hit Minnesota," he said.
The all-night vote count was the latest chapter in a saga created by Wellstone's death in a plane crash 11 days before the election.
The 58-year-old liberal died in the midst of a tough campaign against Coleman for a third term. Mondale, who served two terms in the Senate and four years as President Carter's vice president, was lured out of political retirement to try to hold Wellstone's seat for the Democrats in the closely divided Senate.
The day before the election, an angry Gov. Jesse Ventura appointed fellow Independence Party member Dean Barkley, a major figure in Minnesota's third-party movement, to temporarily fill Wellstone's seat, just as Mondale and Coleman had their only debate of their compressed Senate campaign.
The governor said he was upset that Jim Moore, the party's gubernatorial candidate, was excluded from the televised event.
Coleman, 53, had to remake his campaign when Mondale stepped in. Analysts gave the former St. Paul mayor low chances for success, predicting sympathy for Wellstone and respect for Mondale would combine for a comfortable victory.
But Wellstone supporters handed Republicans a second chance at victory by turning a televised memorial service into a partisan foot-stomp. The scene offended Republicans and some undecided voters, and though Democrats later apologized, the fallout lingered for days.
Coleman launched a statewide travel blitz and latched on to a new slogan, "The future is now" — a not-so-subtle jab at Mondale's 74 years.
Mondale responded with self-deprecating humor. "I've looked into it and there's not much I can do about it," he said of the age question. His campaign aired sober TV ads touting his credentials, including one with the tagline: "Serious Experience."
In addition to the Senate and the vice presidency, Mondale's long career took him to Japan as ambassador. He suffered a landslide defeat to Ronald Reagan in the 1984 presidential race.
Coleman's victory gilded a remarkable night for state Republicans. Minnesota's governor's office went to Republican Tim Pawlenty, a young, suburban lawyer who climbed through the GOP from college intern to state House majority leader. He defeated Democrat Roger Moe to succeed Ventura, an independent who did not seek a second term.