The 20-year-old, who signed a three-year contract with his boyhood club earlier this season, had joined the League Two outfit at the start of the 2019/20 campaign on a season-long loan and made 20 appearances in all competitions.
Watts made his first team debut for the Magpies in their Premier League Asia Trophy clash against Wolverhampton Wanderers in July and the England under-19 international can play in defence and midfield.
He returned to Newcastle at the end of the year for some of his rehabilitation period after he was injured in Stevenage's FA Cup tie against Peterborough United in November.
Despite briefly heading back to the Lamex Stadium, Watts has now returned to St. James' Park following discussions between Newcastle's loan coordinator Shola Ameobi and Stevenage head coach Graham Westley.