The 71-year-old pontiff had an operation on Tuesday to remove the lower lobe of his right lung, fuelling speculation about how his illness might change his 17-month papacy.
Smiling from a window of the Vatican's Apostolic Palace as he spoke to pilgrims below in a firm, clear voice on Sunday, the first US pope thanked people across the world for their prayers and said he would now begin to resume his normal schedule.
"Having overcome this delicate phase ... I will now gradually resume my activities, always with the help of God and your prayers," Leo said.
The pontiff said the experience of the last week "has made me feel especially close to those facing illness and infirmity."
He told the faithful that he had ''truly felt your support," and expressed ''particular gratitude to the doctors, nurses and all the staff at Gemelli hospital" where he was treated.
The pope paused for a moment and waved to the crowd before retreating into his apartment in the Apostolic Palace.
With his return to the Vatican, the Pope's surgeon said there were "no clinical reasons" to cancel his planned trip to Latin America.
"The Holy Father has put his heart and soul into his recovery," Stefano Margaritora told Vatican News, adding that he expected the pope to recover fully from surgery "in another 10 days or so".
Leo is scheduled to make an ambitious November 6-17 trip to Uruguay, Peru and Argentina, including a dozen flights and two helicopter rides to high altitudes.
"As for a long trip involving air travel in about three weeks, I would say there are no clinical reasons why it should not take place," Margaritora said on Saturday.
The Pope's surgery confirmed he had adenocarcinoma, the most common type of lung cancer.
Discharged on Saturday, he greeted patients inside the hospital, before waving to well-wishers outside.
He paused when a 13-year-old Ukrainian girl presented him with a homemade papal doll that she said had helped her through successful cancer treatment.
She had briefly met Leo at an audience in St Peter's Square in December - an encounter she told reporters "gave her the strength to overcome the illness".
Leo has shown signs of recovering well. He had a phone call with Russian President Vladimir Putin, held meetings with senior aides and celebrated Mass in a makeshift hospital chapel.
Margaritora also confirmed the nodule was discovered by chance during routine abdominal examinations. It appeared as "a small spot" at the base of the lung, which extends down to the diaphragm, he said..
He added that if the spot had been higher up, "it certainly would not have been seen".
The cancer was in its early stages, and the Pope had "no respiratory symptoms, and felt perfectly well", Margaritora said.
He described Tuesday's procedure to remove the lobe as "routine" and "without complications" but acknowledged that it "stirred deep feelings ... to operate on a Pope, who for the first time - at least in modern history - is undergoing surgery for a malignant tumour."
Testing of the tumour and related lymph nodes was underway. The results, along with details of the tumour's molecular and genetic makeup, will help doctors determine whether the Pope needs additional treatment.
Options include chemotherapy, a combination of chemotherapy and immunotherapy, or targeted oral therapy based on the tumour's genetic characteristics.
