Rashford, Diogo Dalot, Fred and Luke Shaw were all in the final year of their deals but had an option to extend their contracts by 12 months.
Rashford has rediscovered his form this season under new boss Ten Hag, playing 20 matches in all competitions and scoring nine goals. Dalot, Fred and Shaw have also been heavily involved, each making more than 15 appearances in all competitions.
“Yes, I can confirm it,” Ten Hag told the club’s website in an excerpt from an interview to be published on Tuesday.