The 76-year-old said Benedict XVI had "enriched and invigorated" the Catholic Church. Francis offered the respects while speaking with the cardinals who elected him on Tuesday.
He said Benedict had "lit a flame in the depths of our hearts that will continue to burn because it is fueled by his prayers that will support the church on its missionary path."
Before the start of the meeting, Francis tripped when he got up to meet the dean of the College of Cardinals, but he recovered quickly.
Experts believe the new pope will stay true to his roots as pontiff.
"He is going to be a simple person. He is not going to speak in grand theological terms, he is going to try to say things simply and do things simply," said Vatican analyst John Thavis.
The Associated Press contributed to this report.