"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 statement.
Begich, mayor of Anchorage, led Stevens by 3,724 votes with approximately 2,500 votes left to be counted.
Stevens has served seven terms in the upper chamber. He was convicted last month on charges that he concealed gifts he received from a businessman.
"My family and I wish to thank the thousands of Alaskans who stood by us and who supported my re-election," Stevens said. "It was a tough fight that would not have been possible without the help of so many Alaskans