Yoon is a member of the conservative People Power Party. He won a five-year term beginning in May following a hard-fought election.
During the campaign, Yoon accused outgoing liberal President Moon Jae-in of being more friendly toward North Korea and China than the U.S. He also wanted to have better relations with Japan, even though the countries have been opponents in the past.
Firm against North Korea
"I'll rebuild the South Korea-U.S. alliance," Yoon said in a televised news conference on Thursday. He promised to "establish a strong military capacity" and to "firmly deal with illicit, unreasonable behavior by North Korea."
However, he said, "I'll always leave open the door for South-North talks."
After his victory, the new South Korean leader spoke with U.S. President Joe Biden. The White House said in a statement Biden congratulated Yoon and the two agreed to work together in dealing with threats from North Korea's nuclear and missile programs. In recent weeks, North Korea has tested several new missile and satellite systems.
Yoon said South Korea and Japan should work on building future relationships. The two countries are closely linked economically and culturally. But relations worsened under Moon's presidency over disputes related to Japan's 1910-1945 occupation of Korea.
Japanese Prime Minister Fumio Kishida said Thursday he wants to improve ties between the countries. But he said Japan will not pay any more money to South Korea than it agreed to in a 1965 treaty.
Yoon won the election with a very small number of votes over Lee Jae-Myung, the liberal governing party candidate.
The victory was partly seen as a rejection of Moon's liberal government. Moon's popularity suffered in recent years over failures to deal with economic inequalities, weak job markets and rising house prices. These problems affected many people in their 20s and 30s.
Yoon now has to control South Korea's record-breaking COVID-19 cases and deal with economic issues. He also faces a nation sharply divided by areas of the country, political views, age and gender.
During the campaign, Yoon promised to end the country's Gender Equality and Family Ministry, saying its policies are unfair toward men. Opinion studies released after Wednesday's election showed that his gains in male votes were largely canceled out by young women who voted for Lee.
During Thursday's news conference, Yoon repeated a view that the country no longer has structural barriers to women's success. He said dealing with the pandemic would be of the highest importance for his team.
I'm Jill Robbins.