Chief Cabinet Secretary Yoshihide Suga, long seen as Abe's right-hand man, was chosen Monday as the new head of the governing Liberal Democratic Party, virtually guaranteeing his election as prime minister in a parliamentary vote Wednesday because of the party's majority.
On Wednesday, both houses of the Japanese parliament will hold a vote to name the new prime minister, who will then appoint new ministers.
The entire Japanese government resigned, with each of the ministers submitting requests to Abe, according to Kyodo News.
Abe, Japan's longest-serving prime minister, announced his resignation last month, pointing to a serious health issue that would not allow him to continue leading, even resulting in a number of hospital visits in August.
But while he has championed some measures meant to help rural areas like his hometown in northern Japan's Akita, his political views remain something of a mystery.
He is viewed as more pragmatic than ideological, and during his campaign spoke more about the need to break down administrative obstacles - so-called bureaucratic silos - than any grand political guiding principles.
Suga has said kickstarting the economy will be a top priority, along with containing the virus - essential if the postponed Tokyo 2020 Olympics are to open as planned in July 2021.
"I extend my congratulations to Prime Minister Suga and the Japanese people", he added.
Media reports say some key ministers, including Finance Minister Taro Aso, Foreign Minister Toshimitsu Motegi, Olympic Minister Seiko Hashimoto, and Environment Minister Shinjiro Koizumi, the son of former Prime Minister Junichiro Koizumi, will stay.
Abe's younger brother, Nobuo Kishi, was handed the defence portfolio, while outgoing Defence Minister Taro Kono takes charge of administrative reform, a post he has held before.
If confirmed, that would be fewer than the three women who served in Abe's last government.
Suga has pledged to push forward with Abe's policies including "Abenomics", a mix of measures aimed at beating deflation and spurring growth in the world's third-largest economy.
He will also take over a sweeping review of Japan's national security policy that was initiated by Abe after plans to introduce a USA -developed missile defense system were scrapped due to technical issues. And he will have to establish a good relationship with whomever wins the US presidential race.
Relations with China may prove trickier.
On Wednesday morning as he prepared to resign, Abe said he had given "all my strength" and was ending his tenure "with a sense of pride".