The 20-year-old has left the Magpies' pre-season training camp in Yorkshire to link up with the Pilgrims, who won promotion to League One last season.
Alnwick-born Watts made his Premier League debut as a substitute against Liverpool on the final day of last season, having spent time with Stevenage and Mansfield Town in League Two during the campaign.
The England under-19 international had been an ever-present for Newcastle United's under-23s in 2018/19. Having played in several positions during his Academy career, he has established himself as a ball-playing centre-half over the last two years and signed a new three-year contract with the Magpies last November.
Head coach Steve Bruce, who was keen to include Watts in his first team group in Yorkshire before allowing the youngster to head out on loan, said: "I'm very pleased for him. It's a really good move and I do believe it's the next step in his progression.
"He did well for us at the back end of last season - now let's hope he can go and have a really good season with Plymouth. In terms of his education, it'll do him the world of good."
Watts, speaking to NUFC TV before making the long journey to Devon, added: "I'm delighted. I had two loan spells last year, which were a success, then came back and made my Premier League debut. It just shows that you get monitored when you're on loan and the gaffer spoke to me yesterday and said to go and enjoy it.
"In your career, you never want to be standing still so getting that step up to League One gives me that opportunity of those games - and there's some big clubs in League One that I'm looking forward to playing against. I felt I started last season as a bit of a boy but moving out of home for the first time, going away to Stevenage and Mansfield, makes you grow up fast.
"They're a newly-promoted team and they've made some good signings. I'm glad I'm going a couple of weeks before the season starts so I can meet all the lads, meet the gaffer and get settled in so when the first game comes I'll be ready to go."
