The Japan Rugby Football Union has confirmed that Aso had pledged his commitment to the country's bid and would act as the committee's executive adviser.
Japan insisted the global economic downturn would not have any adverse effect on their bid and the JRFU have already secured corporate backing from some of the country's largest companies, including Toyota, Toshiba and Suntory.
Japan lost out to New Zealand in the race to host the 2011 World Cup and faces competition from England, South Africa, Italy and Australia in the bidding for the 2015 tournament.
Wales, Scotland and Ireland have also expressed an interest in staging the event.
"The support of the government and Japan's financial circle is a big step forward," said former Japanese PM Yoshiro Mori, now serving as the president of the JRFU. "We are confident."
British Prime Minister Gordon Brown has thrown his support behind England's bid, widely believed to be the biggest threat to Japan's hopes of hosting Asia's first Rugby World Cup.
Japan is one of several countries to have bid for both the 2015 and 2019 tournaments.