The boy, who was wearing a track suit and appeared to be about 10 years old, approached the pope at the start of the audience in the Vatican's large Paul VI hall but caused no alarm for security officials, who did not try to stop him.
He shook the pope's hand, jumping up and down in front of him. When it became clear that he wanted to stay for a while, Monsignor Leonardo Sapienza, the head of protocol, got up and gave the boy his chair at the pope's right.
The boy, who the pope later said had a medical "limitation," walked on and off the stage freely, returning to the center several times as the audience continued with the pope reading his address.
He pointed to the pope's white skull cap, known as zucchetto, several times.
His persistence paid off. He was given a zucchetto, prompting applause and laughter from the crowd of several thousand people.
"I thank this boy for the lesson he has given all of us. May the Lord help him in his limitation, as he grows, because what he did came from the heart," the pope said.