The poll, which will come a year early and before the US presidential election in November, will decide which party controls parliament's lower house.
MPs there will meet on Tuesday to confirm Shigeru Ishiba as the country's next prime minister.
"It is important for the new administration to be judged by the people as soon as possible," Ishiba said at a news conference at LDP headquarters in Tokyo.
Ishiba on Monday began picking government and party officials who will contest the general election with him.
Those include two rival candidates in the leadership race, Katsunobu Kato as finance minister and Yoshimasa Hayashi to stay on as chief cabinet secretary, a pivotal post that includes the role of top government spokesman, two sources told Reuters.
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, the sources said, confirming earlier media reports.
Yoji Muto, a former junior minister, will take charge at the economy, trade and industry ministry, a separate source said.
Not included in his picks, however, is Sanae Takaichi, the hardline conservative he beat by 215 votes to 194 on Friday in the closest leadership election in almost seven decades.
Takaichi's absence could make it difficult for Ishiba to manage a fractious ruling group roiled by scandals that have sapped its public support.
Ishiba picked another rival, Shinjiro Koizumi, as his election campaign chief, along with former Prime Minister Yoshihide Suga, a Koizumi backer, who is the party's new vice president. Both joined him at his news conference on Monday.
Ishiba, 67, won the LDP leadership race on his fifth attempt with strong backing from rank-and-file members.
He is however, considered something of troublemaker by many of his parliamentary colleagues for often defying party policy.
Before his run-off election against Takaichi on Friday, he apologised to LDP MPs for his "shortcomings".
