Francis is the first pope to visit DR Congo since John Paul II in 1985, when it was still known as Zaire.
About half of DR Congo's population of 90 million are Roman Catholics.
The 86-year-old Pope, who struggles to walk due to a chronic knee ailment, was lowered from the plane then pushed in a wheelchair onto the red carpet leading to the terminal.
DR Congolese Prime Minister Jean-Michel Sama Lukonde greeted him, then accompanied him as he was wheeled inside.
"For me, it's the first time I'm seeing him other than on television. It's a moment of joy," said Alain Difima, a Catholic priest who spent hours waiting for the Pope's arrival at the airport.
Along Boulevard Lumumba, the long artery that leads from the airport into Kinshasa through some of the poorest neighbourhoods, enthusiastic crowds chanted as they waited to watch the Pope go by.
After a formal welcome ceremony at the presidential palace and a meeting with President Felix Tshisekedi, the pontiff will give a speech to authorities, diplomats and representatives of civil society.
On Wednesday, he will celebrate Mass and meet victims of violence from the eastern part of the country, which is blighted by recurring fighting between rebels from the M23 group and government troops.
"I wanted to go to Goma but we can't because of the war," the Pope told reporters during his flight, referring to a city in eastern DR Congo that he had originally planned to visit before that stop was scrapped because of fighting in the region.
DR Congo has some of the world's richest deposits of diamonds, gold, copper, cobalt, tin, tantalum and lithium but its abundant mineral resources have stoked conflict between militias, government troops and foreign invaders.
Mining has also been linked to inhumane exploitation of workers and environmental degradation.
Eastern DR Congo has also been plagued by violence connected to the long and complex fallout from the 1994 genocide in neighbouring Rwanda.
An estimated 5.7 million people are internally displaced in DR Congo and 26 million face severe hunger, largely because of the impact of armed conflict, according to the United Nations.
The Catholic Church plays a crucial role in running schools and health facilities in the country, as well as promoting democracy.
First scheduled for last July, the Pope's trip was postponed because he was suffering a flare-up of a chronic knee ailment.
Francis will stay in Kinshasa until Friday morning, when he will fly to South Sudan, another country grappling with conflict and poverty.
In a first, he will be accompanied for that leg of his journey by the Archbishop of Canterbury, leader of the global Anglican Communion, and by the Church of Scotland Moderator.
The religious leaders have described their joint visit as a "pilgrimage of peace".
