The approval means the government ploughs ahead with the prime minister's reform platform following the ruling party's landslide electoral victory last month.
The bills met little opposition since Prime Minister Junichiro Koizumi's ruling Liberal Democratic Party and its coalition partner New Komei Party clinched a two-thirds majority in the 480-member lower house in 11 September elections.
The lower house apparently voted along partisan lines, 338-138.
The closely watched legislation now goes to the upper house for approval, which reportedly could vote as early as Friday.
That chamber rejected the proposal in August, prompting snap elections, but officials say the election results have persuaded some former opponents to support the bills.
The legislation would split up Japan Post's delivery, insurance and savings deposit services, and sell them off by 2017.
Largest private bank
The privatisation process would begin in late 2007 and create the world's largest private bank.
Proponents argue the reform would make more efficient use of Japan Post's 330 trillion yen ($3 trillion) in savings and insurance deposits, while streamlining the country's enormous delivery service.
The vote was a major victory for
Prime Minister Junichiro Koizumi
"We can pave the way for a huge fund ... to move from the public sector to the private sector, and about 260,000 full-time workers will be employed by private sector without firing a single person," said Shigeo Oshima, an LDP lawmaker.
"This enables us to create a small government."
The vote was a major victory for Koizumi, who has staked his final year in office on passing the reform.
The postal changes, which he has championed for more than a decade, is part of his larger programme of downsizing government and controlling public spending.
US Treasury Secretary John Snow, in Tokyo for talks with Japanese finance officials, praised Koizumi for pushing through reforms that he said were helping revive the world's second-largest economy.
Japan is just emerging from a decade-long economic slowdown.
John Snow: There is opportunity
for far-reaching reforms
"It offers the opportunity for far-reaching structural reforms," Snow said of the postal privatisation plan.
"We trust and hope that the measure will be successful."
The main opposition Democratic Party of Japan offered an alternative bill that would keep mail delivery and bill payment services under government control, but reduce the savings and insurance deposits controlled by the state.
But the DPJ's legislation was rejected. The Democrats have only 113 seats in the 480-member lower house.
Reform opponents fear the bills will lead to job losses and would put ordinary people's savings in the hands of untrustworthy private investors.
They also argue that privatisation will lead to a reduction in delivery services in sparsely populated rural areas.
"In order to guarantee the rights of the Japanese, those are the businesses that the government should conduct," said Takashi Ishizeki, a DPJ lawmaker who criticised the government proposal in a debate before the vote.