The Liberal Democratic Party elected Takaichi, 64, to regain trust from a public angered by rising prices and drawn to opposition groups promising big stimulus and clampdowns on foreigners.
A vote in parliament to choose a prime minister to replace Shigeru Ishiba is expected to be held on October 15.
The new LDP president is likely to succeed Shigeru Ishiba as leader of the world's fourth-biggest economy because the party, which has governed Japan for almost all the postwar period, is the biggest in parliament.
But this is not assured as the party and its coalition partner lost their majorities in both houses under Ishiba in the past year.
Takaichi, the only woman among the five LDP candidates, beat a challenge from the more moderate Shinjiro Koizumi, 44, the son of popular former prime minister Junichiro Koizumi, who was bidding to become the country's youngest leader in the modern era.
Takaichi won 185 votes to Koizumi's 156.
A former internal affairs minister with an expansionary economic agenda, Takaichi inherits a party in crisis.
Various other parties, including the fiscally expansionist Democratic Party for the People and the anti-immigration Sanseito have been steadily luring voters, especially younger ones, away from the LDP.
"Recently, I have heard harsh voices from across the country saying we don't know what the LDP stands for any more," said Takaichi in her speech before the second-round vote.
"That sense of urgency drove me. I wanted to turn people's anxieties about their daily lives and the future into hope."
Takaichi, who says her hero is Margaret Thatcher, Britain's first female prime minister, offered a starker vision for change than Koizumi and is potentially more disruptive.
An advocate of late premier Shinzo Abe's "Abenomics" strategy to jolt the economy with aggressive spending and easy monetary policy, she has previously criticised the Bank of Japan's interest rate increases.
Such a policy shift could spook investors worried about one of the world's biggest debt loads.
Takaichi has also raised the possibility of redoing an investment deal with US President Donald Trump that lowered his punishing tariffs in return for Japanese taxpayer-backed investment.
Her nationalistic positions - such as her regular visits to the Yasukuni shrine to Japan's war dead, viewed by some Asian neighbours as a symbol of its past militarism - might rile South Korea and China.
She also favours revising Japan's pacifist postwar constitution and suggested that Japan could form a "quasi-security alliance" with Taiwan, the democratically governed island claimed by China.
If elected, Takaichi said she would travel overseas more regularly than her predecessor to spread the word that "Japan is Back!"
Takaichi is expected to hold a media conference later on Saturday.
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