SEOUL, South Korea -- Moon Jae-in, a longtime opposition leader who favors opening a dialogue with North Korea, is claiming victory as South Korea's next president, ending a decade of conservative rule.

Moon, 64, from the progressive Democratic Party, is leading in exit polls by a large margin over his two main rivals, conservative Hong Joon-pyo and Ahn Cheol-soo.

So far, 75 percent of the votes have been counted, with Moon garnering 39.8 percent, Hong at 25.7 percent and Ahn at 21.4 percent. Hong and Ahn have already conceded. The official announcement of the winner will be made early Wednesday morning.

Moon is replacing former President Park Geun-hye in a by-election after she was impeached in March. Her five-year term was to end in February 2018, but after a series of political scandals, she is in jail awaiting trial on charges of corruption.

Born to a poor family that fled North Korea and settled in a small island in South Gyeongsang province, Moon started his career as a radical pro-democracy activist and a human rights lawyer.

He served as a senior secretary to then-President Roh Moo-Hyun from 2005 to 2006, then as his chief of staff from 2007 to 2008.

Moon's administration is expected to take a softer approach in dealing with North Korea, signaling a possibly turbulent ride for U.S.-South Korea relations.

Public sentiment in South Korea has begun to sour toward Washington after President Trump said last month that Seoul should be paying for the Terminal High Altitude Area Defense (THAAD) missile defense system, contradicting an agreement between South Korea and the U.S. in which Seoul would provide only land and infrastructure support. The progressives voiced discontent, saying that the U.S. bullied South Korea into hosting the system and then demanded the country foot the $1 billion bill.

Moon said the previous conservative government's hard-line approach to North Korea failed to prevent Pyongyang from developing nuclear bombs and missile programs. He favors engagement and greater dialogue. He repeatedly pledged during his campaign that South Korea would have an independent voice in the international community.

North Korea has consistently supported Moon's victory, with its state media on Tuesday encouraging South Korean voters to "judge the puppet group of conservatives."

The new administration will likely reopen the Kaesong Industrial Complex, an inter-Korean industrial park in North Korea, which Park shut down last year to increase pressure on Pyongyang.

ABC News' Yoo Hong and Sooji Nam contributed to this report.