The President was among those greeting the 33 miners as they were successfully brought to the surface last week after 69 days underground.
As he visited Number 10 today, President Pinera presented Mr Cameron with a lump of rock from the floor of the cave, while gifts presented by the PM included bottles of ale for each of the miners.
During their meeting, the two leaders also discussed trade, the global economy and creating a low carbon economy.
A Downing Street spokesman said:
The Prime Minister met President Pinera of Chile this afternoon. The Prime Minister began by congratulating President Pinera on his leadership throughout the crisis at the San Jose mine. The rescue last week had inspired the world.
The Prime Minister and the President then discussed how best to enhance the commercial and diplomatic relationship between the UK and Chile. They agreed to work together to increase bilateral trade and share expertise on low carbon economic growth. There was also agreement to work together on the global economy. The PM made clear to President Pinera that the UK would remain a true friend of Chile.