Shift foreman Luis Urzua is the last miner to be rescued. His voice was the first heard when the men were found.
A specially made capsule had been carrying the men one by one to the surface. Officials said the operation had gone faster than expected.
Each of the miners was greeted with cheers and then tears as they were re-united with their families.
All the freed miners are being taken to a triage centre for health checks. Some of them will have to have emergency dental surgery.
All of them are being checked for skin infections and respiratory conditions after more than two months in 30C heat and humidity of 85%.
One of the miners, who has not been named, is suffering from pneumonia.
The men have been trapped underground since 5 August, when a rockfall caused a tunnel to collapse.
The rescue operation began shortly after 2315 on yesterday (0215 GMT on today) with a technical expert, Manuel Gonzalez, being lowered down the 624m (2,047ft) shaft.
Mr Gonzalez was supposed to return to the surface and report on the condition of the rescue shaft, before handing over to a paramedic.
However, a live video feed from the refuge where the miners were gathered showed Mr Avalos getting into the “Phoenix” capsule. He was chosen to lead the way because he was one of the fittest of the miners.
Mr Avalos reached the surface at 0010 (0310 GMT) and was greeted by his family, rescuers, President Sebastian Pinera and the first lady, Cecilia Morel.
Chilean President Pinera called the mission “magical.” U.S. President Barack Obama called it a “tremendously inspirational story.” (CNN/BBC)
