The US authorities arrested Ashe, who was General Assembly president for a year from September 2013, in October for allegedly accepting USD 1.3 million in bribes from a Chinese billionaire real estate mogul.
They also charged him with tax evasion. He had been in plea talks as recently as last month.
The current assembly president, Mogens Lykketoft, expressed his "sincere condolences" to Ashe's family.
"Despite the many as yet unproven accusations made against him, Mr Ashe was for many years a hard-working and popular member of the diplomatic corps in New York and at the United Nations," he said in a statement.
His arrest was a major blow for the UN, which is seeking to promote corruption-free good governance worldwide.