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.

Scott Diver, 16, from Clydebank, West Dunbartonshire, was last seen at his home on Saturday 17 September.
The teenager, who is 5ft 7in tall, with a slim build, dark hair and blue eyes, is said to need regular medication.
The CCTV images show Scott walking in Clydebank's Dalmuir Park, towards the Mountblow Road entrance, at about 14:53 on the day he went missing.
Insp John Mullen said: "The two images we are issuing today have been identified as Scott - this is the last confirmed known sighting of him.
"As the weather was favourable that day, there were a number of people within the park who may have seen Scott.
"I would urgently ask anyone who remembers being in the park and who might have seen Scott to get in touch with us. Even if you don't believe you may have seen Scott in the park please contact the police as you may have information that is pertinent to our inquiry."
Insp Mullen said that given the length of time Scott had been missing police and his family "remain concerned for his welfare".
He added: "His family and friends are very distressed at his disappearance. He is a young boy who is vulnerable and needs to be home with his family."
Insp John Mullen said that anyone with information could contact police at a dedicated email address: scottdiverinquiry@scotland.pnn.police.uk

The 21-year-old scored twice for the non-league team in their FA Cup first-round defeat by Carlisle in November.
Morais has previously played in the Football League for Wycombe.
"He has scored some great goals already this season for St Albans, and we are pleased to have secured his signature," said Posh boss Grant McCann.
Media playback is not supported on this device

A test transmission has already begun on Freeview channel 23 in south east Wales.
The broadcaster will be based at Elgin House in St Mary Street in the city centre and will have around 20 staff.
The Made TV group holds licences for local TV in Cardiff, Bristol, Leeds, Middlesbrough and Newcastle.
The other two local TV stations in Wales, Bay TV Swansea and Bay TV Clwyd in Mold, are both due to launch in 2015.
Made in Cardiff will shortly appear on the Sky satellite TV service in the area on channel 134, and Virgin Media channel 159.

Alan Bennett, of Lingholme, Redcar, was at Teesside Magistrates' Court for the short hearing during which he confirmed his name and address.
He is accused of murdering Lynne Freeman, 46, and 30-year-old Jodie Betteridge, on Wednesday evening.
He was remanded in custody and will appear at Teesside Crown Court on 29 March.
Police were called to Mapleton Crescent, where Mrs Freeman lived on Wednesday evening, then seven minutes later to Ms Betteridge's address in Byland Close.
Ms Freeman's children Sarah Helm, 28, James Helm, 27, Kimberley Helm, 25 and Lauren Freeman, 18, previously said in a statement: "We shouldn't have to be writing a tribute to our mother who was taken from us so early. She should still be here to watch her four kids and grandkids grow."
In tribute to Ms Betteridge, Theresa Largan, 51, said: "Jodie lived for her kids. I don't think I ever saw her on her own, she always had the tribe with her."
Pope Francis has been presented with the Copa Libertadores trophy by players and officials of Argentine side San Lorenzo.
[NEXT_CONCEPT]
Police have released new CCTV images of a vulnerable teenager who has been missing for more than two weeks.
[NEXT_CONCEPT]
Peterborough United have signed striker Junior Morias from National League South side St Albans for an undisclosed fee on a two-and-a-half year deal.
[NEXT_CONCEPT]
Cardiff's local TV channel, Made In Cardiff, has announced that it will begin broadcasting programmes on 15 October at 20:00.
[NEXT_CONCEPT]
A man has appeared in court accused of murdering two women within minutes of each other in separate attacks.