Aso, who was the favourite to take the party leadership, won 351 out of 527 votes to win Monday's first round contest.
Kaoru Yosano, minister for economic and fiscal policy, was runner-up in the election with 66 votes.
"Mr Taro Aso won a majority. As the result, we have decided that Taro Aso has been elected," Hideo Usui, the party's election administration chief, said.
After winning the vote, Aso said: "I express my gratitude that this election was held fairly."
"From this moment on, there is no conflict among the five candidates who ran in the election."
Economic challenge
Should Aso be elected Japan's prime minister on Wednesday he will replace Yasuo Fukuda, who resigned this month amid plummeting approval ratings.
Aso, a Catholic with a reputation as an outspoken conservative, has vowed to turn around Japan's sagging economy and defend its national interests by strengthening Japan's alliance with the US.
Aso is now widely expected to call snap general elections - possibly for as early as late October - in the hope of thwarting an increasingly popular opposition.
"He is quite determined to make sure that he has the mandate of the people. He has already announced that he will be calling a general election; the date will be set at a later point," Marga Ortigas, Al Jazeera's correspondent in Tokyo, said.
"The opposition party here is quite hopeful that the LDP will actually lose seats in the next general election, because they are determined to show the LDP that the fact that two prime ministers from that party resigned in two years is irresponsible and that it is time for a new government."
Aso is seen as a stark contrast to Fukuda, who was reluctant to engage with the opposition and was seen as having problems connecting with voters.
But his opponents have criticised his plans to boost the economy by stepping up government spending.
"He has made statements before that he wishes to increase government spending and he wants to inject more money into the local economy," Ortigas said.
"He has said that he wants to cut taxes while at the same time trying to focus on the health care and social services systems here."
Last year the LDP, which has ruled Japan almost continuously since 1955, lost control of the upper house of parliament for the first time.