In the tape, the pilot had earlier asked for priority to land due to fuel problems and the request was granted by Medellin's international airport.
Authorities are still investigating what caused the charter flight to crash in the mountains outside Medellin as it carried Cinderella-story team Chapecoense Real to a major match.
A haunting recording aired by Colombian media appeared to hold answers -- though officials have not confirmed its authenticity.
"Ma'am, LAMIA 2933 has a total failure, total electrical failure, without fuel," pilot Miguel Quiroga tells the control tower in the recording, minutes before the jet crashed Monday night.
In the tape, the pilot had earlier asked for priority to land due to "fuel problems."
The request was granted by Medellin's international airport.
But the control tower then lost contact with the plane, whose fuselage was found plastered on a hillside 50 kilometers (30 miles) outside the city.
The crash killed most of Chapecoense's squad and 20 journalists traveling with them to the finals of South America's second-largest club tournament.
The unsung Brazilian club was on the way to crowning a fairytale year in the Copa Sudamericana against Medellin side Atletico Nacional.
Announcing the crash on Monday night, the aviation authority said the plane had reported electrical problems.
But it may also have been out of fuel.
A Colombian military source told AFP: "It is very suspicious that despite the impact there was no explosion. That reinforces the theory of the lack of fuel."
The plane was scheduled to make a refueling stop in Bogota, but skipped the Colombian capital and headed straight for Medellin, reported Bolivian newspaper Pagina Siete, citing a representative of the airline.
"The pilot was the one who made the decision," Gustavo Vargas of Bolivian charter company LAMIA told the newspaper.
"He thought the fuel would last."
Colombia's civil aviation authority said it hoped to establish the cause of the crash "as soon as possible."
British and Brazilian investigators headed to Colombia to help with the probe, authorities said.
Investigators have recovered the black boxes from the British Aerospace 146 plane.
They were undamaged and "will reveal everything," said Colombian Transport Minister Jorge Eduardo Rojas.
Bolivian civil aviation chief Cesar Varela told reporters "the crew had their licenses in order. Everything was in order."
Hometown fans in the southern city of Chapeco, population 200,000, were in shock.
"Chapeco is not a big city. We would meet (the players) in the street," said teacher Aline Fonseca, 21.
"It's hard to keep going," she said. "The city is devastated."
Fans gathered Wednesday evening in the Chapecoense stadium, which was draped in black ribbons, and in Atletico Nacional's stadium in Medellin at the time the match was to have been played.
Both stadiums were packed to capacity.
Mourners, many dressed in white, held candles in the air in Chapeco as the handful of remaining players from the team took the pitch in tears.
Brazil has declared three days of national mourning.
Other Brazilian clubs have offered Chapecoense players so it can continue competing. Special funds have also been set up.
The Spanish football league said next Saturday's blockbuster clash between Barcelona and Real Madrid will be preceded by a minute's silence for the crash victims.
Six people miraculously survived the crash. Three were footballers, but goalkeeper Jakson Follmann had his right leg amputated, said the hospital treating him.
Two flight crew and a journalist also survived.
Four people missed the flight.
They included Chapeco mayor Luciano Buligon, who arrived Wednesday in Medellin to oversee the return of the bodies along with Brazilian Foreign Minister Jose Serra.
Brazil's ambassador in Colombia, Julio Glinternick, told AFP authorities hoped to have identified all the bodies by Thursday morning.
So far, 42 have been identified, according to Brazil's foreign ministry.
The Brazilian air force will then fly them home in two Hercules cargo planes.