Aso, a wisecracking conservative who clinched the presidency of the ruling party earlier this week, was all but guaranteed to be elected prime minister later in the day. His Liberal Democratic Party dominates the powerful lower house of parliament.
Fukuda had announced he would step down three weeks ago after only a year in office, citing slumping support ratings and the strain of dealing with strong political opposition.
Parliament was to hold a vote in both houses later Wednesday. Aso was expected to lose in the upper house, which is controlled by the opposition, but win in the lower house, which has the final say. He was expected to then set up his new Cabinet and hold a late night press conference.
With Aso's ascension widely seen as a certainty, attention Wednesday turned to who he would tap to serve in his administration.
Kaoru Yosano, who ran against Aso in the latest race, was expected to keep his previous post in charge of economic and fiscal policy. Former defense minister Shigeru Ishiba, another opponent, was widely reported to be Aso's choice for agriculture minister.
Shoichi Nakagawa, a former economic minister, was seen as the leading candidate to become the new minister of finance.
Aso, 68, and his Cabinet will take office in tumultuous times.
The former Olympic skeetshooter - and Japan's first Catholic leader - will inherit a government wracked by scandals, paralyzed by gridlock and divided over how to deal with growing economic instability.
The parliamentary vote Wednesday should reflect the turmoil. The opposition-controlled upper house is expected to vote for Ichiro Ozawa, the leader of the minority Democratic Party of Japan.
The LDP-run lower house, however, will most likely vote for Aso, requiring a lengthy parliamentary process to sort out the impasse in which the ruling party by force of numbers will triumph.
Once in office, Aso will confront political and economic difficulties.
One of the first things on the agenda will be deciding whether to call early elections for the lower house to prove his party - which has governed for nearly all the past 53 years - still has a mandate to rule.
Such an election would be a major gamble for the party, which is bleeding public support and suffering widespread anger over mismanagement of pension funds and a general dissatisfaction with the status quo.
Elections can be called by the prime minister at any time, but must be held by next September.
The economy will be another challenge. Growth has stalled, ending a lengthy expansion, and inflation is picking up. The financial meltdown in the United States threatens to pull Japan down with it.
He has also said that he will continue to place relations with Washington as Japan's top diplomatic priority, while trying to improve ties with neighboring China, whose growing economic and military clout Aso once described as a "major threat."