Rashford's United and England debuts were separated by just 92 days, though the 18-year-old found the net on both in a stunning start to his career.
Eight goals in 18 games at Old Trafford, as well as that maiden strike against Australia in Sunderland last week, was enough to convince Roy Hodgson to call-up Rashford.
And Rooney believes Rashford is here to stay, praising the way his fellow striker has handled his meteoric rise to fame.
He told a news conference: "The way he took to coming into the Man United team and the way he's performed from then until the end of the season has been incredible for his age and he's certainly showed what he can do in his first game for England, couple of minutes got his first goal.
"What's pleasing is his attitude, it's first class and that's shown round the hotel and on the training pitch, Roy's chosen him and he deserves it so he could be a real positive for us.
"It's great for the team and the squad that Roy's got options as strikers and midfield, a lot of attacking options that you need going into the tournament."
Rooney believes he can lead England's young squad - one of the tournament's least experienced - to success, and is confident that he is in the best possible shape to do so.
"It's a proud moment for myself to captain the team in a tournament," the United skipper added.
"It's a young squad but it's got a lot of quality.
"I've said in the last two years, I'm really excited to be in this team. Nothing's changed, I'm excited to lead the team and I really believe we've got a good squad to do well."
He continued: "I'm injury free. I feel a lot of tournaments, not all of course, but a lot I've had little niggles so I'm happy with my fitness and my form and just looking forward to the tournament."