Henman, who made the Wimbledon semi-finals four times during his career, praised Murray for his discipline in the sport.
"I was privileged enough to go into the locker room straight after the match and Andy was basically in a state of shock," Henman told BBC Sport. "I just gave him a big hug when I got in there and said 'I really don't know how you did that' and he said 'nor do I'.
"It's just an incredible achievement and the magnitude of what has happened is still sinking in. He is such a student of the game that he can remember all of his results from the juniors, he remembers all the matches he has played, the shots he has made, but he had no recollection whatsoever about that final game today. It was just a blur.
"I spoke to all his team in the locker room and there was champagne being sprayed everywhere. It was an amazing day for Andy, an amazing day for tennis and an amazing day for British sport."
Murray has now won two Grand Slams during his career after his US Open victory last year.