They were discovered by two British divers on a ledge in a cavern after a marathon search operation in the Tham Luang caves in Chiang Rai.
The challenge now will be to extract the party safely, with rising water and mud impeding access.
Families of the missing group were ecstatic at news of the rescue.
Rescuers had hoped they would find safety on a ledge in an underground chamber nicknamed Pattaya Beach but they were found 400m (440 yards) away having moved to higher ground to avoid the rising water.
How did they find them?
The two British rescuers are believed to be Rick Stanton and John Volanthen, who arrived in Thailand early last week.
It took them several hours to reach the group on Monday.
In video posted on Facebook by Thai Navy SEAL special forces, one can be heard speaking in English to the group, as they sit on a ledge above water in a cavern, picked out by torchlight.
"How many of you?" the rescuer asks.
"Thirteen!" comes the reply.
The group appear to ask when they will be taken to safety and one of the unseen rescuers replies: "Not today. There's two of us. We have to dive. We are coming. OK? Many people are coming. We are the first."
One of the boys is heard to say: "Eat, eat, eat, tell them we are hungry."
When the group, whose voices are indistinct, ask what day it is, the divers pause, then one replies, "Monday, Monday. You have been here... 10 days. You are very strong."
The divers explain that they have to leave but will be back.
"Thank you so much," says one of the huddled group. "Where you come from?"
"England. The UK."
"Oh. See you tomorrow."
The group's plight has gripped the country and led to an outpouring of support.
The boys aged 11 to 16 and their coach went to explore the caves on 23 June.