The 19-year-old was invited on trial with the Magpies last month and impressed coaches to win a two-year contract.
Smith started his career at Scottish Premiership champions Celtic before joining Scottish League Two side East Fife.
The Coatbridge-born goalkeeper made 28 appearances last season, making him one of the youngest senior goalkeeper in British football.
He becomes United’s seventh summer - and the club’s fourth academy signing - behind Charlie McArthur, Alex Murphy and Jordan Hackett.
“I’m buzzing to be signing for Newcastle United,” Smith told nufc.co.uk “After playing in the lower leagues of Scotland, I couldn’t be happier with the opportunity to go and play for a club like Newcastle.
“I was playing part-time at East Fife last season so it’s a great opportunity to be full-time with Newcastle. It’s an unbelievable chance for me to go and develop my career further so it was a no-brainer for me to join.
“Playing for East Fife’s first-team was good experience, especially at a young age, and playing mens’ football did me the world of good. I just want to be playing week in week out, especially as a goalkeeper.
“It’s the next chapter in my life which I’m looking forward to and really hope to kick on.”