“I would be lying to say that I’m not disappointed to have lost the record,” Charlton, 79, told the United website.
“However, I can honestly say that I’m delighted for Wayne. He deserves his place in the history books.”
He continued: “He is a true great for club and country, and it is fitting that he is now the highest goalscorer for both United and England.
“It has been great to watch him every week since his arrival at Old Trafford in 2004; he set the tone with a wonderful hat-trick on his debut and he has thrilled us all in the years since, going on to enjoy a hugely successful career.
“I was 35 when I retired. Wayne is only 31 and still going strong, so I don’t think he’s done by a long stretch yet. He continues to show that he can contribute goals, assists and performances whenever called upon. He will raise the bar even further before he calls it a day.
“Now he’s the man to beat, and I can’t see anybody doing that for a long, long time.”
“Wayne thoroughly deserves his place in the history books of this great club and I am sure that he will go on to score many more goals.”
Current United boss Jose Mourinho said: “It is the record of the biggest club in England and one of the biggest in the world.
“Before him the record belonged to a legend of English football. Now Wayne becomes a legend of Manchester United.”
Stoke boss Mark Hughes, who had two spells as a striker with United said: “It is an outstanding record and won’t be surpassed. It has taken 40-odd years for Sir Bobby’s record to be broken which shows how high a mark it was.”
Rooney, 31, said he was honoured to break the record.
“I am very proud,” he told Sky Sports. “It is not something I expected when I joined. I am proud and I hope there is more to come.
“The players who have played for this club have been world class. I am proud to play for this club and to be all-time goalscorer is a huge honour.”
Asked about Charlton by Gary Lineker for the BBC’s Match of the Day, Rooney added: “He’s such an iconic figure, and has been for so long. When you sign for the club, you realise how important he is. To surpass him in goals is something I never thought I’d do. I have the utmost respect for him.
“He came and congratulated me in the dressing room so I know he’s pleased in some way.
“I’m a team player but records are important. When you finish your career you can look back on it and it’s something to tell your kids.”
“An incredible achievement”
Manchester United and England team-mate Michael Carrick hailed Rooney’s longevity and ability to bounce back from criticism.
“It is tough to play so many games and have that scrutiny on you constantly, and how he has dealt with that and answered back, and how he has shut people up when they have questioned him, he is still going strong and it is not easy to do,” the midfielder told BBC Radio 5 live’s Sportsweek.
“When he burst on to the scene he was so hungry and aggressive and explosive. He has calmed that down but he is quality in and around the box, to find that pass or that finish. He has done it all his career – 12-13 years – and to do it for so long is an incredible achievement and shows how good he is.
“I have seen more of Wayne than others like Bobby Charlton, Denis Law and George Best. They are all icons and legends, not just for Manchester United but for football in general, and Wayne is right up there with the best of them. For him to get the record for club and country is an incredible achievement and something he should be proud of.”
Former England manager Sven-Goran Eriksson, who had urged the media not to “kill” Rooney when he left as national boss in 2006, called him a great player.
“He’s still a fantastic player. He’s clever and can play in different positions. He can play as striker, second striker, winger, midfielder,” said the Swede.
Current England boss Gareth Southgate told the Football Association official website: “When you look at whose record he has broken and the way Sir Bobby is revered in this country and by his club, it shows you what an achievement it is.
“To have scored that many goals you have got to have performed so consistently over such a long period of time, which is a mark of an outstanding player. Wayne has managed to achieve that.”