Rooney netted a second-half penalty as England overcame Switzerland 2-0 in a Euro 2016 qualifying match on Tuesday, having already equalled Charlton's record in the 6-0 win over San Marino on Saturday.
And following the match, the England captain hailed Hodgson for helping him on the way to the record, speaking of his delight at finally surpassing Charlton's long-standing goal tally.
"Since Roy's come in I've scored a lot of goals under Roy and I'm grateful for him for letting me play with the freedom which I enjoy," Rooney told ITV Sport.
"It's a great feeling [being England's record goalscorer]. Obviously I've known I've been close to it the last few England games to finally do it is a dream come true.
"As you've probably seen I was emotional out there so [it is] a huge honour, something I'm extremely proud of.
"I'm happy it's done and hopefully we can kick on from here and concentrate on the team and hopefully have success in the future."
The England forward also admitted that there have been some testing times in an England shirt, but said that reaching the record was a dream come true.
"You play each game and each year as it comes really and I went through a spell round about 2008 where I didn't score for a couple of years I think for England," he added.
"It's right up there, if not the best [achievment]. Being the country's all-time leading goalscorer before the age of 30 is something I could never have dreamt of, and I'm just extremely proud of tonight."
Rooney, who broke the record with a second-half penalty, indicated that he planned to hit the spot kick with as much power as he could muster, in the hope of finding the net.
"I knew myself it was a big moment for me and I just picked my corner and put my boot through it, to get as much power on it as possible and make it hard for the goalkeeper," Rooney continued.
"The goalkeeper got a touch on it but thankfully it had too much power so I'm grateful for that."