Johnson finished with a all-time record aggregate of 268 (-20) for his four rounds as he claimed his second major in spectacular style on Sunday at Augusta National.
That was two shots better than the previous record held jointly by Woods and Jordan Spieth who shot 270 in 1997 and 2015 respectively.
Harmon coached Woods between 1993 and 2004 during which time he burst into the big time to establish himself as one of the greatest golfers of all time.
The two had a close relationship with Harmon acknowledged as a major influence on the rising star who went on to win 15 majors.
Speaking after watching Johnson claim the green jacket, Harmon said: “When he’s firing on all cylinders, like he was this week with his driving and controlling his irons, he’s the closest thing to Tiger Woods I’ve ever seen.
"The difference to that is that Tiger was on for the best part of 20 years, so he’s got a way to go to get in that category!
“I think it meant so much to DJ that it was Tiger who put the green jacket on him after winning this great tournament. He grew up just 75 miles from Augusta, so this is a tournament he always wanted to win.”
2002 PGA Championship winner Rich Beem was also full of praise for Johnson, saying that a career grand slam was within his grasp.
“Butch Harmon has no doubts that Dustin will win more majors, but I am going to go one more than Butch," he said.
"I think Dustin Johnson in the next three years is going to win the career grand slam.”
***See the 2021 Masters LIVE on eir sport next April.