( 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 ca n't wait to get to work fighting for Alaskan families . '' CNN political producer Ed Hornick contributed to this report .
NEW : `` It is apparent the election has been decided , '' Sarah Palin says . NEW : Gov . Stevens congratulates Stevens , praises Stevens . Republicans bested Stevens by 3,724 votes , according to posted results . Anchorage mayor had roughly 48 percent of vote vs. roughly 48 percent for Stevens .