Abe, who led the LDP to a landslide victory in the general election after three years in the opposition, will form a new Cabinet later in the day with his close allies.
After parliament formally installed him as Japan's seventh premier in six years, the 58-year-old will be replacing Yoshihiko Noda of the Democratic Party.
Abe told reporters that by drawing on his experience of heading a government, he did like to run his new government in a stable manner.
According to the Japan Times, Abe has given the post of finance minister to former prime minister Taro Aso, who dealt with the 2008-2009 global financial crisis with fiscal stimulus measures.
In the hope of implementing fiscal and financial programmes effectively to tackle Japan's chronic deflation, the 72-year-old Aso, who was prime minister when the LDP was ousted from power by the DPJ, will concurrently serve as deputy prime minister, finance minister and financial services minister, the report said.
Yoshihide Suga, 64, one of Abe's closest partners, will be appointed as chief cabinet secretary.
Abe will be the second man to serve twice as premier in post-World War II Japan, after Aso's grandfather Shigeru Yoshida in the 1940s and 1950s.
According to the report, with China's maritime ambitions and North Korea's rocket launches perceived as a threat to the security environment in East Asia, Abe has promised to strengthen Japan-US ties and enable Tokyo to exercise its right to collective self-defence with Washington.