In Wednesday's vote, Hatoyama won 327 of the 480 votes in the lower house.
"I'm thrilled with the joy of creating history, and at the same time I feel the very grave responsibility for creating history," Hatoyama told reporters.
His first task would be to name a cabinet.
Media reports said he has already chosen Katsuya Okada – who has never held a cabinet post - as his foreign minister and Hirohisa Fujii as his finance minister.
Fujii was finance minister under a coalition government in 1993-94, the only time - albeit briefly - in its 55-year history that Aso's Liberal Democratic party had previously been out of power.
Hatoyama, who is expected to be formally endorsed by Japan's emperor later on Wednesday, has a limited pool of seasoned politicians to choose from.
The DPJ, created a decade ago, has never held power, and nearly half of the Democratic members of the lower house will be serving in their first term in parliament.
Despite the relative lack of experience, Hatoyama has said he wants to build a foreign policy that will put Tokyo on a more equal footing with Washington and forge closer ties with Japan's Asian neighbours, particularly China.
Some members of Hatoyama's party have said they want to overhaul the US-Japan security alliance under which 50,000 US troops are deployed throughout Japan.
But the top US military commander in Asia is confident about continuing strong ties with the new government.
Admiral Timothy Keating, who heads the Hawaii-based Pacific Command, said on Tuesday that he would travel next week to Tokyo for discussions with Hatoyama's government.
"I'm very confident, almost certain, that there will be - maybe some discussions about certain aspects of US-Japan military alliance - but writ large no significant change," Keating said in Washington.
"We've had a treaty with Japan for over 50 years. They're a strategic linchpin for us in the Western Pacific and I'm not concerned about any big changes."