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.

The Ocean's Eleven stars will premiere '50s-set crime comedy Suburbicon at the event, which Damon stars in and Clooney co-writes and directs.
Damon will also be seen in festival opener Downsizing, directed by Alexander Payne.
After premiering three major Academy Award winners in a row, Venice is seen as a good luck charm for the Oscars.
Previous films to debut at the event include Birdman and Spotlight, which went on to win the Academy Award for best picture.
Last year's opener La La Land was also named best picture - but only as the result of an envelope mix-up.
In Suburbicon, Damon character tries to understand the dark mysteries of his seemingly peaceful town along with wife Margaret, played by Julianne Moore.
In Downsizing, which also stars Kristen Wiig, Neil Patrick Harris and Jason Sudeikis, he plays a man who literally shrinks himself in search of a better life.
Guillermo Del Toro will debut his other-worldly fairy-tale The Shape of Water. Set against the backdrop of America's Cold War era, it stars Sally Hawkins, Michael Shannon and Octavia Spencer.
Darren Aronofsky will also premiere his latest film Mother!, starring Jennifer Lawrence and Javier Bardem.
The director said he was "excited" to be unveiling the horror film, which will also screen at Toronto.
Chinese contemporary artist and activist Ai Weiwei will also be competing in the festival with his film Human Flow, a film about the global refugee crisis.
Spanning 23 countries over the course of a year, the film focuses on both the scale of the crisis and its personal human impact.
Weiwei said: "There is no refugee crisis, only a human crisis. The border is not at Lesbos, but really it is in our hearts and minds."
Jane Fonda and Robert Redford will be celebrated with the Golden Lion lifetime achievement award at the festival.
Netflix film Our Souls at Night, in which they both star, will be premiered out of competition.
Alberto Barbera, the festival's artistic director, called Fonda "one of the great protagonists of contemporary international cinema" and Redford "a thoughtful, instinctive actor with a keen sense of detail."
New to this year's festivities is Venice Virtual Reality, billed as the first competition for VR works at a major film festival.
The 74th edition of the Venice Film Festival runs from 30 August to 5 September.
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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).
[NEXT_CONCEPT]
George Clooney and Matt Damon are set to bring some Hollywood glitz to this year's Venice Film Festival.