The 67-year-old former defence minister, who won a close-fought contest last week to lead the ruling Liberal Democratic Party (LDP), was confirmed as prime minister by parliament on Tuesday.
He is scheduled to hold his first press conference later on Tuesday in Tokyo.
Fumio Kishida announced in August he would resign as Japan's prime minister at the end of his term. (AP PHOTO)
The Ishiba administration's approach to diplomacy with Japan's closest ally, the United States, will be in focus, as he has repeatedly called for a more balanced relationship with Washington.
He has also proposed creating an Asian version of the collective security group NATO to deter China, an idea that could draw ire from Beijing and has already been dismissed by a senior US official as hasty.
Ishiba must quell simmering anger over rising living costs and his scandal-plagued party, and navigate a volatile security environment in East Asia fuelled by an increasingly assertive China and nuclear-armed North Korea.
The veteran lawmaker, seen as somewhat of a party outsider who failed at four previous leadership bids, has named a mix of rivals and allies and to a cabinet of 20 ministers that includes only two women, fewer than half the previous administration.
They include two leadership rivals in key positions - Katsunobu Kato as finance minister and Yoshimasa Hayashi to stay on as chief cabinet secretary, a post that includes the role of top government spokesman, the government announced.
The appointment of Kato, a proponent of former premier Shinzo Abe's "Abenomics" expansionary fiscal and monetary policies, appears to be a balancing act to alleviate concerns over the next cabinet's economic strategy.
The Nikkei stock index fell almost five per cent on Monday in reaction to a surging yen following Ishiba's win over Sanae Takaichi, a monetary dove and fiscal expansionist, in Friday's leadership contest.
The index recovered ground on Tuesday.
Shigeru Ishiba has proposed creating an Asian version of security group NATO to deter China. (AP PHOTO)
Kato's appointment to the finance ministry will be closely watched given he served in key positions in former premier Shinzo Abe's administration, which pursued expansionary fiscal and monetary policies.
The Nikkei stock index fell almost five per cent on Monday in reaction to a surging yen following Ishiba's win over Sanae Takaichi, a monetary dove and fiscal expansionist, in Friday's leadership contest.
The index recovered ground on Tuesday.
A close Ishiba ally, Takeshi Iwaya, a former defence chief, will take over as foreign minister, while Gen Nakatani will return to the defence ministry, a position he held in 2016.
Yoji Muto, a former junior minister, will take charge at the economy, trade and industry ministry.
Five of the MPs who contested the leadership race with him have not been included in his government nor given key party jobs.
Among them is Takaichi, a hardline conservative he beat by 215 votes to 194 on Friday in the closest leadership election in almost seven decades.
Local media reported she had declined a senior party post.
Despite its troubles, the party which has ruled Japan for most of the post-war era remains likely to hold on to power in the October 27 election given Japan's weak opposition.
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