The teenage trio have come through the club's youth system and featured for the U18s last season.
Striker Brayson, who's father is also a Newcastle academy graduate, told the club's website: "My dad has played a massive part because he's went through the same journey as me so to follow in his footsteps is unbelievable and I'm buzzing.
“Signing a professional contract is what I've been working for and it's a good step forward."
Defender Craggs was named Newcastle's Scholar of the Year last season and said: "I was buzzing to even get my scholarship so to be nominated as the best in the club's group for how I am as a person, both on and off the pitch, means a lot.
"I really appreciated all the staff who nominated myself as I was proud of the fact that they valued me as a person and how I applied myself in the education side of the scholarship."
And fellow defender Watts also stated: "I was over the moon (to sign a first professional contract) because, ever since I joined the club at under-12 level, that's what I've been aiming for.
"Once I got a scholarship, I was pushing for that pro contract and then when I signed it, I was delighted.