It was England's first Grand Slam since 1995 and their fourth final-hurdle Grand Slam clash in five seasons under Woodward.
All three previous encounters were failed missions - against Wales (1999), Scotland (2000) and Ireland (2001) - but Woodward's players made amends in magnificent fashion.
He said: "We put a lot of pressure on ourselves all week and I am delighted for the players.
"I can't say how good these guys are. They're the toughest guys I've ever been involved with both physically and mentally.
"It was a huge day for us. The whole country should be very proud of them. It sets up 2003 for us."
He added: "I was confident we were going to win if we kept the ball. Ireland are a great team.
"The players deserve this big time. A lot of hard work went into this today.
Skipper Martin Johnson said the sweet smell of victory washed away the stench of previous failures.
"We have had disappointments over the years and there was a lot of pressure on both teams but we came through," he said.
"Great credit to our players and the coaches who have worked so hard. Credit to the Irish boys too, but we have finally done it."