The former United defender revealed the news on his Instagram page, sharing an image of his boy, who turned 16 on Tuesday, holding up a Red Devils shirt.
Ex-England full-back Neville captioned: "Proud of you Harvey Neville. Go follow your dreams!"
Harvey also took to Instagram to share the news, posting a picture of himself signing his contract.
He wrote: "I am very proud and excited to have signed for the club I have supported my whole life."
Gary Neville also passed on his best wishes, posting: "Congratulations Harvey Neville you've practised so hard to get where you are! Keep going."
When Phil took over as a coach at Valencia, Harvey signed for the youth team as a midfielder or a winger and garnered a reputation from free-kicks and corners.
The former Everton star made 386 appearances for United after graduating from the youth team over an 11-year period.
He then swapped Old Trafford for Goodison where he went on to play 303 times before hanging up his boots in 2013.
Gary Neville, Harvey's uncle, played his entire career for United, featuring 602 times for the Red Devils.