Marcus Rashford and Cameron Borthwick-Jackson committed their future to United after signing four-year contracts, with an option to extend them by a year.
Rashford has been in fine form for the 20-time English champions as he scored eight goals in 18 appearances in all competitions.
“He is still very young and we need to be patient, but he is developing in the right way and we believe he has a great future ahead of him,” Woodward told United’s official website.
“I am delighted that Marcus has signed a new contract, he is at the right club to continue his development. Marcus is a naturally talented footballer with great potential. He has taken his chances well and has integrated into the first team very quickly.”
His club form has seen him make it to England’s 26-man provisional squad for Euro 2016. The striker took 138 seconds to score his first goal on his international debut in the Three Lions’ 2-1 win over Australia.
Wright: England should take Rashford to France
Meanwhile, Arsenal legend Ian Wright is hoping that Roy Hodgson includes Rashford in his 23-man squad for the European championship.
“I certainly don’t think it is anything like the gamble some feel. How can it be, based on what we’ve seen so far? Every time this kid has been presented with a challenge, he’s rolled up his sleeves, met it head on . . . and come out smiling,” Wright told The Sun.
“His goalscoring record is there for all to see. Just 18 club games and eight goals – with an FA Cup final win in there, too. Then, when he made his senior international bow last week, he takes just 138 seconds to become England’s youngest ever debut goalscorer.
“But what has impressed me above everything else is the way he has handled it. No fuss or frills, just get the job done and move on. I really wouldn’t be surprised if it got even better, and he was given a place in Roy’s final 23.”