He was 90.
Saxena's brother Naresh Chandra, former Cabinet Secretary and Ambassador to the US, said he was rushed to a hospital in the wee hours after he complained of breathlessness.
He was declared dead at 4:30 AM, Chandra said. He was born in Agra in 1928 and is survived by his wife and two daughters.
Saxena, who also headed country's external intelligence agency RAW, took charge as the Jammu and Kashmir Governor for the first time on May 26, 1990 and continued in the post till March 13, 1993. He was re-appointed in 1998.
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He was RAW Director between 1983-86.
Saxena came to J&K at a time when the entire Kashmir Valley was facing a turmoil following killing of Mirwaiz Maulvi Farooq by militants of terror group Hizbul Mujahidden.
During the Mirwaiz's funeral, the mob went on rampage and security forces had to open fire in downtown Srinagar to control the situation. Nearly 25 people were killed.
"No militancy can be fought without the local police," he had said when he was the Governor in the second term.
Chandra recalled that 10 days back his brother, while being wheeled out from Intensive Care Unit (ICU) of a private hospital, had held the hand of the doctor and said "I don't have any stress other than the happenings in Jammu and Kashmir.
His funeral will be held later today.
Former J&K chief ministers Farooq and Omar Abdullah condoled his death saying that in his departure, a visionary has been lost.
"I recall my association with Governor Saxena. He was very cool in extreme situations and always had a humane approach to any problem," Farooq said.
Omar, who became a Member of Parliament in 1998 and 1999, said, "It's a sad news for me. He (Saxena) had always guided me during my initial days in politics."