A pope and prophet from the separate Christian religions had never met before in person.
Francis, 82, and Nelson, 94, sat down for a 33-minute talk, which included issues of "mutual concern."
"We talked about our mutual concern for the people who suffer throughout the world and want to relieve human suffering," Nelson said. "We talked about the importance of religious liberty, the importance of the family, our mutual concern for the youth of the church, for the secularization of the world and the need for people to come to God and worship Him, pray to Him and have the stability that faith in Jesus Christ will bring in their lives."
Russell Ballard, acting president of the Quorum of the Twelve Apostles, also attended the meeting and met with members of the media.
Ballard,90, emphasized work on humanitarian projects.
"We explained to His Holiness that we work side by side, that we have projects with Catholic Relief Services all over the world in over 43 countries," Ballard daid. "[We've] been shoulder to shoulder as partners in trying to relieve suffering. He was very interested in that."
The historic meeting with the Catholic pontiff for the world's 1.2 billion Catholics brings more recognition to the globe's 16 million Latter-day Saints, which the church formerly referred to as Mormons.
"We had a most cordial, unforgettable experience. His Holiness, he was most gracious and warm and welcoming," Nelson said. "What a sweet, wonderful man he is, and how fortunate the Catholic people are to have such a gracious, concerned, loving and capable leader."
On Sunday, the church dedicates its first temple in Rome.