Shares of the state-owned firm and its units were up between 16% and 42%.
The IPO was the biggest in the world this year and the largest since Alibaba's record $25bn deal in 2014.
It also marks the Japanese government's largest asset sale in nearly three decades.
The listing is part of Prime Minister Shinzo Abe's plans to boost the flagging economy by encouraging consumers to invest in the stock market.
About 10% of each company was sold to the public in the largest privatisation of a state-owned firm since Nippon Telegraph and Telephone in 1987.
The government allocated 80% of the shares to domestic investors, with the remaining 20% sold to international institutional investors.
Japan Post Holdings opened at 1,631 yen per share, 16.5% above the IPO price of 1,400 yen. The banking unit started at 1,680 yen, up almost 16% from its IPO price, while the insurance unit was 33% higher.
That compares with a rise of over 2% for the benchmark Nikkei 225 index.
Angus Nicholson, market analyst at trading firm IG, said the "blockbuster" IPO was helping drive the rally in Japanese markets as they returned from a holiday on Tuesday.
"It is a significant moment as the privatisation of Japan Post had been a rallying cry during former Prime Minister Junichiro Koizumi's reign in the early-2000s," he said.
The government plans to raise a total of 4tn yen in additional asset sales in the coming years.
It has said the funds will be used to help reconstruct areas hit by the 2011 earthquake and tsunami disaster.
Shares of Japan Post and its banking and insurance units surged on their stock market debut in Tokyo after the triple initial public offering (IPO) raised $12bn (£7.7bn).