The Anchorage Daily News reported Monday that Begich, 46, formed an exploratory committee in February and has been essentially campaigning ever since then.
"What I've been hearing is people are truly ready for change," Begich said. "They want to see something different."
Begich, a Democrat, said he will not resign as mayor during the campaign.
"This city continues to run because we've got great people working," Begich said. "You'll still see me at the Assembly meetings, still see me engaged with the activities of this city."
In a statement, Stevens, who has been in the U.S. Senate since 1968, said the race will be about experience.
"As I have said before, this race will be about who has the experience, the seniority and the proven record to best serve Alaska in the U.S. Senate," Stevens said.
The newspaper reported that Begich has raised more than $267,090 in campaign cash, mostly from Alaska.
Stevens has about $1.3 million in his campaign account.