Ishiba, 67, says he intends to call a general election for Oct. 27. He won a tight race on Friday to lead the Liberal Democratic Party (LDP), which has governed almost constantly for decades.
Japan's parliament, where the LDP has a majority, approved Ishiba's appointment Tuesday, followed by the announcement of his Cabinet, whose 19 ministers included two women.
Former chief cabinet secretary Katsunobu Kato was named finance minister, while Gen Nakatani took defense and Takeshi Iwaya foreign affairs.
Ishiba, who has held at least three previous ministerial posts, is a self-confessed defense "geek" who tried and failed four times before to become LDP leader.
He finally succeeded this time because, while a divisive figure within the party, he is -- unlike predecessor Fumio Kishida -- relatively popular among voters, analysts said.
Ishiba's win "indicates that the LDP sought an experienced leader with broad voter appeal to steer the party in the next national election," said Yuko Nakano of the Center for Strategic and International Studies.
"If the ruling coalition secures a fresh mandate (in the election), Ishiba will have the opportunity to reshape the party's internal dynamics and restore public confidence, while addressing Japan's broader challenges, including economic stagnation felt by many voters and regional security concerns," she said.
Tumbling stocks
Markets, however, have reacted negatively, with the Nikkei plunging almost 5% on Monday. On Tuesday, the index recovered some ground and closed up 1.9%.
Ishiba's backing of interest rate hikes by the Bank of Japan has sent the yen higher, while the prospect of corporate tax hikes has worried investors.
One major area of government spending is the military.
Kishida undertook to double defense spending and boost ties with the United States.