The Tottenham Hotspur forward fired home shortly before halftime to give England a 2-0 lead and move past Rooney with whom he had shared the record.
Kane's goals have come in just 81 appearances whereas Rooney scored 53 times in 120 games.
"This means everything," Kane said. "So excited to get back out there and put the England shirt back on. And it had to be a penalty of course. Once it hit the back of the net there was so much emotion. Just huge thanks to the players, staff and fans."
"Congratulations to Harry Kane on becoming England's all-time leading goalscorer. I knew it wouldn't take long but that was quick. Great man, unbelievable goalscorer and an England legend. Congrats Harry!" Rooney said on Twitter.
It was a special moment for the England captain who had the chance to break the record in the World Cup quarter-final against France but missed a penalty in the 2-1 defeat in Qatar.
It is the second scoring record Kane has broken this season having gone past Jimmy Greaves's haul of 266 goals for Tottenham last month. He now has 271 for the London club.
Tributes poured in for Kane on social media after his achievement.
"Many congratulations to Harry Kane on becoming England’s highest-ever goal-scorer. A wonderful achievement," Gary Lineker tweeted.
"Congratulations Harry Kane, England's all-time top goal scorer," Alan Shearer wrote.
