Ibrahim El Bakraoui blew himself up in the check-in hall of Zaventem airport while Khalid El Bakraoui attacked a metro train at Maalbeek station near the EU headquarters, Frederic van Leeuw told a news conference.
Prosecutors said the confirmed toll from the two attacks was 31 dead and 270 wounded.
Van Leeuw said Bakraoui's "will" said he was "in a rush", and "I don't know what to do ... Hunted everywhere ... No longer safe", adding that "I don't want to end up in a cell next to him".
The computer on which Ibrahim wrote the will was dumped in a trash can in the same street in the Brussels district of Schaarbeek where investigators found an unexploded bomb, an Islamic State group flag and bomb-making materials last night.
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Prosecutors confirmed that they had found 15 kilos of TATP high explosive in the flat.
They also found chemicals including 150 litres of acetone, 30 litres of liquid oxygen, detonators, a suitcase full of nails and other bomb-making equipment including plastic trays, tools and ventilator.
"The third man is on the run; he left his bag with the biggest bomb in it, which exploded later because it was so unstable. This third person remains unidentified and is still being looked for," he said.