The 21-year-old plays full-back, centre or wing and already has four caps for Los Pumas, having shone for his country at Under-20s level.
Scoring five tries in 27 matches during his two seasons with Bristol, the 6-foot-2 star hails from the city of Salta.
Also able to kick goals, he continues a rich tradition of Argentina players representing Newcastle, with countryman Franco Molina also joining the Red Bulls for next season.
Sporting general manager Neil McIlroy said: “Benjamín is an outstanding young talent with skill and athleticism in abundance.
“He has already made his international breakthrough and has a couple of Gallagher PREM seasons under his belt, but there is plenty more to come from him.”
Elizalde said: “I'm excited to start a new chapter with Newcastle Red Bulls, and I'm looking forward to being there and meeting everyone.
“It’s an honour to join a club with such a rich history and strong identity.
“I’m truly grateful for the opportunity and am ready to give my all, to grow as a player and contribute to the team’s future.”
BENJAMÍN ELIZALDE BIOG
Position: Full-back/centre/wing
Born: 14/6/2004
Height: 1.88m (6 foot 2)
Weight: 95kg (14 stone 13)
Honours: Argentina