SEOUL—A conservative former top prosecutor was elected South Korea’s new president in one of the closest fought races in recent history, which will shape Asia’s fourth-largest economy for the next five years. Yoon Suk-yeol, 60, from the main opposition People Power Party, edged out the ruling Democratic Party’s Lee Jae-myung with 48.6 percent of the vote to 47.8 percent, with around 99.3 percent of the ballots counted as of 5 a.m. on Thursday. Yoon said he would honor the constitution and parliament and work with opposition parties to heal polarized politics and foster unity, calling the election a “victory of the great people.” “Our competition is over for now,” he told a news conference, thanking and consoling Lee and other rivals. “We have to join hands and unite into one for the people and the country.” Lee had conceded defeat and congratulated his opponent. “I did my best, but failed …