Harry Kane came on for his England debut against Lithuania
Rooney, only two goals behind Sir Bobby Charlton's England record of 49, starts up front with the 21-year-old.
"I'm as excited as everyone else in the country about Harry. He's had an unbelievable season," said Rooney.
Kane won his first cap as a second-half substitute for Rooney in the [Only registered and activated users can see links. ] at Wembley on Friday, and scored 79 seconds after coming on.
"Going into the season, there were even questions about whether he would start for Tottenham," added Manchester United captain Rooney, who also scored against Lithuania.
"He was starting Europa League games but not the Premier League games - but he gave his manager Mauricio Pochettino no option but to play him and he's not looked back, scoring goals every week."
How England might warm up for Euro 2016
England look set to play friendlies against France, Spain, Germany and the Netherlands should they qualify for Euro 2016.
The FA is hoping to arrange games against France at Wembley on 17 November and away to Spain later that month.
A match against world champions Germany has been agreed for March 2016, while discussions are taking place to arrange a game against World Cup semi-finalists the Netherlands prior to the tournament.
The speed of Kane's development is illustrated by the fact that he did not make his first league start of this season until 9 November, when he played in Spurs' 2-1 home defeat by Stoke City.
However, he had scored 29 goals in all competitions for his club before getting his first England goal on Friday.
Rooney added: "It's exciting for this group of players to train with him. After his goal on Friday, I bet he can't wait to get out on the pitch and try to get another goal.
"It's great for English football to have someone scoring so regularly in the Premier League and getting a goal on his debut at full international level. It's an exciting time for him and all of us."
Kane is set to face Italy defender Giorgio Chiellini, bitten by Luis Suarez during last year's World Cup
But Rooney said Kane faces a sterner test against battle-hardened Italy defenders such as Giorgio Chiellini, the player bitten by Luis Suarez during their World Cup defeat against Uruguay in Brazil last June.
He warned the Tottenham striker that Italy's defenders will use their experience and street-wisdom to try to frustrate him.
"They're clever defenders," said Rooney. "They do anything to try to stop you and you have to be aware of that and not get frustrated.
"Harry must continue what he is doing. He's taking the ball, running at defenders and getting shots at goal - that's all he has to do on Tuesday. If he does that the way he has been doing, he'll be fine."
While Kane is pushing his case to become a regular for England at senior level, Gareth Southgate still intends to take the striker to this summer's European Under-21 Championship.
England Under-21 manager Southgate said: "Roy and I know that the seniors are in a good group position and he feels that the experience of going to the Czech Republic in the summer will be more beneficial to Harry than the two games the senior team have got.
"That is absolutely the case regardless of his displays between now and then.
"We still feel we can give the players the best possible preparation to go into the seniors and achieve success if they have got the experience of the European Under-21 Championship behind them. That is still the case with Harry."