The pontiff has supported the Buenos Aires-based team since he was a boy.
A delegation travelled from the Argentine capital to the Vatican with the trophy.
San Lorenzo recently won the Copa - South American club football's most prestigious competition - for the first time in the club's 106-year history.
Earlier in the week, Pope Francis said: "I am very happy about it, but, no, it is not a miracle.
"For me, San Lorenzo was the team all my family supported. My father played in the basketball team and when we were kids, we sometimes went to the stadium with mum," he added.
San Lorenzo beat Paraguay's Nacional 1-0 on 13 August to secure a 2-1 aggregate victory.
Pope Francis has been presented with the Copa Libertadores trophy by players and officials of Argentine side San Lorenzo.