The firefighters died while fighting the blaze threatening the town of Yarnell, about 80 miles north-west of Phoenix.
The fire was started by lightning on Friday and spread rapidly amid high heat, low humidity and strong winds. At least 200 homes were burned.
Arizona and other parts of the western US – including California – had near-record temperatures over the weekend.
It is the highest death toll for firefighters in a single incident since 9/11.
Arizona Senator John McCain said the families of the dead firefighters were in the thoughts and prayers of all Americans.
“This devastating loss is a reminder of the grave risks our firefighters take every day on our behalf in Arizona and in communities across this nation. Their sacrifice will never be forgotten,” he said in a statement.
Arizona Governor Jan Brewer said it could take “days or longer” to reveal how the deaths occurred.
“This is as dark a day as I can remember,” she said.
“It has been confirmed that 19 wildland firefighters have lost their lives on the Yarnell Hill fire Arizona,” the US Wildland Fire Aviation said in a statement.
The firefighters were part of a specially trained “hotshot” unit who had battled other wildfires in New Mexico and Arizona in recent weeks, officials say.
They were forced to deploy emergency tent-like structures meant to shield them from flames after becoming trapped and “something drastic” happened, said Dan Fraijo, fire chief in the nearby city of Prescott.
“One of the last fail-safe methods a firefighter can do is literally to dig as much as they can down and cover themselves with a protective fire-resistant material, with the hope that the fire will burn over the top of them and they can survive it,” he said.
“Under certain conditions there’s usually only sometimes a 50% chance that they survive. It’s an extreme measure that’s taken under the absolute worst conditions.”
Two other members of the elite unit who suffered severe burns have been flown to a burn treatment centre in Phoenix.
The tragedy is the worst in a wildfire since 1933, when at least 25 firemen died battling a fire in Griffith Park, Los Angeles.
Some 200 firefighters are still battling the fast-moving wildfire, which has grown to 1,000 acres. Additional reinforcements have been called in.
The blaze has forced the evacuation of local residents.
An estimated 200 homes were destroyed in Yarnell, the Associated Press reported, almost half the properties in the town.
In recent days, dozens of people across western US states have been treated for exhaustion and dehydration, as the heat wave continues.
Temperatures in some areas were expected to reach 130F (54C), close to the world’s all-time high recorded 100 years ago in California’s Death Valley.
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