Jill Biden's first husband, Bill Stevenson, called cops about a domestic dispute at his Delaware home and was there when authorities pronounced his wife dead ... TMZ has learned.

Law enforcement in Delaware tells us Bill is the one who picked up the phone and dialed 911 on Sunday night and was waiting at his Oak Hill home when responding officers arrived.

Cops found Bill's wife, 64-year-old Linda Stevenson, unresponsive in the living room and tried life-saving measures before pronouncing her dead at the scene. Dispatch audio from the incident mentions "cardiac arrest."

Detectives from the New Castle County Police Department's Criminal Investigations Unit are handling the death investigation ... but no criminal charges have been filed against Bill, at least not yet.

Police tell us Bill has spoken with detectives and, as of now, is cooperating with law enforcement.

A cause or manner of death has not been determined and Linda's body is awaiting an autopsy.

Jill married Bill in 1970 but they separated in 1974 and went through a nasty divorce ... and in 1977 she married Joe Biden.