During his trip, Pope Francis will beatify Korean Catholics who died for their faith and attend a Catholic youth festival.
The South Korean Catholic Church is one of the fastest growing in the world, with just over 5.4 million members, some 10.4% of the population.
North Korea fired short-range rockets off its east coast around the time of the Pope’s arrival.
It fired three rockets on Thursday morning as the pope’s plane approached South Korean airspace, and another two in the afternoon, according to news agencies.
Pyongyang has engaged in several such launches in recent months in what it says is a response to US and South Korean provocations – in the latest case, a military drill due to start on Monday.
South Korea’s President Park Geun-hye was at the airport to greet the pontiff.
The pontiff is expected to pay tribute to some of South Korea’s first Catholics when he beatifies 124 Koreans who died in the 18th and 19th Centuries.
After an individual is beatified, he or she is given the title “blessed”.
The beatification ceremony will be held on Saturday at Gwanghwamun Square in central Seoul, with up to one million people expected to attend.
Pope Francis is also attending Asian Youth Day, a festival for young Catholics from across the region.
He is also scheduled to meet students who survived the Sewol ferry disaster that claimed more than 300 lives.
A Mass for Peace and Reconciliation will be held in the Myeong-dong cathedral in Seoul on Monday, on the final day of his trip.
There Pope Francis will deliver a message of peace for the divided Koreas and East Asia, according to Yonhap News Agency.
North Korea rejected an invitation by the Archdiocese of Seoul for 10 North Korean Catholics to attend the final mass, South Korean officials say.
It is not clear how many Catholics there are in North Korea.
According to a UN Human Rights Council report released in February 2014, apart from the few organized state-controlled churches, Christians were prohibited from practicing their religion and were persecuted.
The trip is the first visit by a pope to Asia in almost 20 years. Pope Francis is due to visit again in January when he travels to Sri Lanka and the Philippines, one of only two Asian countries with a Catholic majority – the other being East Timor.
Pope John Paul II was the last pope to visit South Korea in 1989, where he prayed for reunification between the North and the South.
Meanwhile, on his way to South Korea Pope Francis also sent a telegram to China’s leaders, a tradition when the pontiff flies over a country.
“I extend my best wishes to your excellency and your fellow citizens, and I invoke divine blessings of peace and well being upon the nation,” the telegram said.
The Vatican has no ties with Beijing, which does not recognize the Vatican’s authority and runs its own Catholic Church.
The last time a pope visited the region, he had to avoid Chinese air space.
In what a Church spokesman has called “a sign of detente”, the papal plane was given permission to use Chinese air space.
More than 100 Chinese people were due to attend Asian Youth Day, but about half were unable to attend due to “a complicated situation inside China”, said a spokesman for a committee organizing the Pope’s visit.
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