Mr. Noda, who as finance minister has steered the nation's economy through one of its most difficult periods, was approved in both the lower house, where his Democratic Party of Japan has a solid majority, and in the opposition-controlled upper house.
Outgoing Prime Minister Naoto Kan and his Cabinet resigned earlier Tuesday, making way for Mr. Noda to name his own team later this week.
LDP lawmakers on Monday elected Mr. Noda as party leader to replace Mr. Kan, who stepped down amid widespread criticism of his handling of the crisis caused by a massive earthquake and tsunami in March.
After his election, Mr. Noda made an immediate plea for unity in his divided party. Addressing party lawmakers from both chambers at a Tokyo hotel, he called on the Democrats to close ranks and stop bickering as they face tough challenges.
Mr. Noda stressed the importance of cooperation in addressing the nation's troubled economy, recovery from the March disasters, and ending the nuclear crisis from the damaged Fukushima power plant.
As an ally of the outgoing Mr. Kan, Mr. Noda is likely to continue many of his predecessor's policies. He is also considered a staunch supporter of the Japan-U.S. security alliance.
In Washington, a spokeswoman for the U.S. State Department, Victoria Nuland, said the United States is looking forward to continuing close cooperation with Japan and its next prime minister across a broad range of issues.
Mr. Noda will have to deal with a deeply divided parliament. While the ruling party has a solid majority in the lower house, the upper house is in the hands of the opposition Liberal Democratic Party and in a position to block any legislation.
Mr. Noda is expected to seek a coalition with the Liberal Democrats and a third party, but it is not clear whether the LDP will be willing to cooperate.
More than 20,000 people are dead or missing from March's earthquake and tsunami, and thousands more have been displaced from homes near the Fukushima nuclear plant.
Across Japan, homes and factories are operating on reduced power as the government conducts safety tests on all of the country's nuclear reactors.