(CNN) -- Alaska Sen. Ted Stevens, the Republican lawmaker convicted on felony corruption charges in October, officially conceded the Senate race to Democrat Mark Begich on Wednesday.

"Given the number of ballots that remain to be counted, it is apparent the election has been decided and Mayor Begich has been elected," Stevens said in a news release.

"It was a tough fight that would not have been possible without the help of so many Alaskans -- people who I am honored to call my friends. ... I wish Mayor Begich and his family well. My staff and I stand willing to help him prepare for his new position," he added.

Alaska Gov. Sarah Palin also congratulated Begich on Wednesday.

"I extend my congratulations to Mark Begich and his family. This is a new era for Alaska, and I look forward to working with Mark on the many issues that are important to our state. I am confident he will add a compelling new voice to the U.S. Senate," Palin said in a statement.

Palin praised Stevens, saying his "tireless efforts on behalf of the state he loves have benefited all those who call it home."

With 100 percent of Alaska's precincts reporting, Begich, the mayor of Anchorage, had roughly 48 percent of the vote, compared with about 47 percent for Stevens, according to CNN's latest tally.

He bested Stevens by 3,724 votes. Alaska Elections Director Gail Fenumiai said that 2,500 overseas ballots remain to be counted.

The full results will be certified during the week of December 1.

A recount could take place, however, if the vote difference between Begich and Stevens is less than 0.5 percent. Stevens could have also asked for a recount, regardless of the difference, if he pays for it himself.

The results of this race have national implications as Democrats seek a filibuster-proof 60-member majority in the Senate. With Begich's win, they hold 58 seats; races in Minnesota and Georgia are still unresolved.

Stevens, who turned 85 on Tuesday, was convicted in October of filing false statements on his Senate financial disclosure forms. Prosecutors said Stevens hid hundreds of thousands of dollars in "freebies" from an oil-field services company in his home state.

On Tuesday, his fellow Senate Republicans postponed a vote on whether to kick Stevens out of their caucus pending the final vote results.

Stevens maintained his innocence even after the conviction. At a debate days before the election, he said he had "not been convicted of anything."

In his statement claiming victory, Begich said he was "humbled and honored" by the apparent results.

"It's been an incredible journey getting to this point, and I appreciate the support and commitment of the thousands of Alaskans who have brought us to this day," he said in the statement. "I can't wait to get to work fighting for Alaskan families."

CNN political producer Ed Hornick contributed to this report.

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