Moon made the announcement during a televised press briefing.
Moon announced during a televised press briefing that he appointed former vice finance minister Kim Dong-Yeon as deputy prime minister and finance minister, while a UN senior adviser on policy Kang Kyung-Wha was named as the foreign minister.
Kang, who has been working at the United Nations since 2006, was the best candidate poised to "raise the status of our diplomacy by with her abundant experience on the international stage and strong initiative", said Moon.
"She has often been referred to as the first and the best female foreign affairs expert so it is significant in terms of gender equality in the Cabinet as well," he added.
As his national security advisor, Moon appointed Chung Eui-Yong, a former diplomat-turned-lawmaker who acted as his top foreign policy advisor during his campaign for the presidency.
While the post is traditionally held by a military official, Moon said: "In the face of North Korea's nuclear threats, I believe the role of diplomacy is ever more important for our security."
The South Korean president also named Moon Chung-In, an honorary professor at Seoul's Yonsei University, and Hong Seok-Hyun, former head of mass-circulated JoongAng Ilbo daily, as his special advisors for diplomatic and security issues.
"The two advisors will discuss with me the new government's diplomatic and security policy direction," Moon said.
Left-leaning Moon favours engagement with North Korea to bring it to the negotiating table, but after a recent missile launch said dialogue would be possible "only if Pyongyang changes its behaviour".
The new leader also begins his term facing multiple domestic challenges, including the aftermath of the huge corruption scandal that saw his conservative predecessor Park Geun-hye impeached and swept him to power, but left the country bitterly divided.