Moyes, who gave Rooney his debut at Everton in 2002 and worked with the 28-year old at Old Trafford last season, believes that he will be successful in his new roles.
"It is a terrific time for Wayne professionally and he is ready for it," Moyes told The Sun. "At this time in his career, I am sure he wants to take on that extra responsibility the captaincies bring. It could make him an even better player.
"He wants to show that development, he has proved he is a top player, now he will want to show he can take on the responsibility and be a top captain.
"He has always been a very determined person, determined to prove himself. He has proved himself a great player, now he will want to prove himself as a great captain and I think he will. He will want to lift trophies for United and England."
Rooney will lead England out for their first Euro 2016 qualifier against Switzerland in Basel this evening.