Once it's certain the capsule is operating smoothly, the 10 sickest men will be lifted. Finally the healthiest will brought to the surface.
"We began to talk to them about the proper order of rescue and they were fighting against us yesterday because every one of them wanted to be at the end of the line, not at the beginning," Chilean Minister of Health Jaime Manalich said Sunday.
It's expected that the last man up will be Luis Urzua, the man who was shift foreman when the collapse occurred and has shown inspiring leadership throughout the ordeal.
When the men reach the surface, they will have to wear sunglasses to protect their eyesight from the glare of daylight.
The miners have been trapped almost a half mile underground since August 5. Getting them out has been an epic struggle, the most technologically challenging mine rescue ever attempted.
Three drills using three different technologies raced to finish a rescue shaft. This weekend it happened.
The so-called Plan B drill, an American-made Schramm T-130 water will borer, broke through to the men early Saturday.
Drill operator Jeff Hart was brought in from Afghanistan to help in the rescue effort.
Hart said the area where the mine was located is one of the toughest terrains to drill and the crews took extra care to ensure safety of both the rescuers and the miners.
"You take a more personal approach to it," he said.
A bell announced the breakthrough to the miners' families at the makeshift camp outside the mine gates. What followed was a spontaneous celebration, but it will no doubt be dwarfed by the celebration that will follow the rescue of all 33 men.
When the disaster began, mining officials thought that rescue wouldn't be possible until December. Drilling has proceeded faster than expected, giving hope to the families waiting eagerly for their loved ones' return.
Now, for the final critical moments, the engineers and officials overseeing the rescue have tried to take every precaution possible.
In anticipation of that moment, engineers lined the top 300 feet of the shaft overnight with steel casing because of concerns about loose rocks falling on the rescue capsule.
The miners' families are counting the final hours. Liliana Ramirez, the wife of Mario Gomez, the oldest miner, said that she is anxious, but happy too. She said that she is "happy that this nightmare is coming to an end."
The men, excited to see their loved ones, want to look their best. They've asked for shampoo and shoe polish.
The men who have endured misery few can imagine want to look presentable to their families after waiting so long see them and wondering if they would ever see them again.
Sources at the rescue site tell ABC News that the men spent their final day underground signing souvenir Chilean flags for their rescue workers.
They've collected rocks and other mementoes to bring up with them at 'Camp Hope.'
The tent city outside the mine gates is a carnival-like atmosphere as families and the massive international press corps counted down the hours until the miner's escape to freedom.
With so much of the world following every twist and turn in this complex rescue, the Chilean government is broadcasting a seven-camera live satellite feed of the rescue for all to see.
But Maria Jose Gomez just wants to see her father. He is 63-year-old Mario Gomez, the oldest of the miners.
When asked what her words would be to her father, Maria said in Spanish: "I believe at that moment there will be no words… only hugs."
The Associated Press and Reuters contributed to this report.