Stevens, who served seven terms in the Senate, thanked thousands of Alaskans for their support and wished Begich and his family well in his concession letter.
"I am proud of the campaign we ran and regret that the outcome was not what we had hoped for," he wrote.
"I am deeply grateful to Alaskans for allowing me to serve them for 40 years in the U.S. Senate," he added. "It has been the greatest honor of my life to work with Alaskans of all political persuasions to make this state that we all love a better place."
The loss of Stevens, the longest serving Republican in Senate history, marks the downfall of a Washington political powerhouse and Alaska icon who couldn't survive a conviction on federal corruption charges.
Begich was declared the victor Tuesday after a tally of just over 24,000 absentee and other ballots gave him 146,286, or 47.56 percent, to 143,912, or 46.76 percent, for Stevens.
FOX News' Serafin Gomez contributed to this report.