The meeting is also intended to underscore the importance the White House places on Japan-US relations as the US president moves to ease concerns that his administration may be tilting towards the rising power of China.
During last year's presidential campaign Hillary Clinton, now US secretary of state, said that the US and China would be "the most important bilateral relationship in the world in this century".
But during her first foreign visit to Tokyo last week, she appeared to revise that stance, noting that bilateral relations between the United States and Japan were "a cornerstone" in US policy around the world.
Aso's arrival in the US comes just days after Clinton's visit to Japan last week [AFP]
Japan, which has the world's second largest economy, trails only China as the largest foreign holder of US treasury bonds, holdings that help finance the ever-growing US budget deficit.
Obama's meeting with Aso will bring together leaders with starkly different political fortunes - Obama is currently enjoying worldwide popularity, while Aso is struggling to stay in power.
Aso is facing single-digit approval ratings, appeals from his own party to resign and the worst Japanese recession in 50 years.
His administration reached a low point last week when his finance minister stepped down after appearing to be drunk during a world finance ministers' meeting in Rome.
Al Jazeera correspondent Tony Cheng, reporting from Tokyo, said the Japanese leader will be hoping that his meeting with Obama will provide a much-needed boost in domestic support.
Asian security issues are also likely to be discussed in Tuesday's talks at the White House.
The United States is Japan's main Asian ally and stations more than 40,000 troops in the country.
It is also working with the US and three other countries to press North Korea to dismantle nuclear programme.
While Aso's visit is expected to focus on the global economy, he may also use the occasion to voice international concerns about protectionist sentiment in the United States.
"Prime Minister Aso will say that Japan will resolutely fight all protectionism," Kazuo Kodama, the press secretary of Japan's foreign ministry, told AFP news agency.
Japan, Canada and the European Union objected when the US Congress drafted a bill saying that infrastructure projects designed to kick-start the US economy could only use US-made manufactured materials.
But after appeals by Obama, it was later altered to say that such measures could only take place in a manner consistent with Washington's international treaty obligations.