The prominent republican was shot dead by members of the Parachute Regiment in the Markets area of Belfast in 1972.
The HET has also revealed the 24-year-old was unarmed when he was shot but he was regarded by the security forces as a dangerous terrorist.
Their report said: "The HET considers that Joe's actions did not amount to the level of specific threat which could have justified the soldiers opening fire in accordance with the Army Rules of Engagement or their standard operating procedures."
The family has welcomed the findings but said many questions still remain unanswered.
Mr McCann's daughter Nuala said: "The shooting of our father was not justified. It was unjustified."
Soldiers from the Parachute Regiment shot Mr McCann several times as he ran away in Joy Street, a mainly nationalist housing area near Belfast's city centre.
The incident happened just weeks after Bloody Sunday.
Mr McCann's wife Anne welcomed the findings.
"It's very hard to relive ... it's still very painful," she told UTV.
"The thing about a sudden death is that it never goes away. But we always knew that what happened to Joe wasn't right."