Sky Sports News understands the deal to be worth £29.5m.
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The 24-year-old full-back becomes the sixth senior addition of the summer and will wear the No 37 shirt at St James' Park.
Dedic, who can operate on either flank, previously worked with Newcastle head coach Matthias Jaissle at Red Bull Salzburg and Liefering.
"Working with Matthias again was a big factor for me," Dedić said. "We know each other well, he knows what I can bring on the pitch and I'm really happy to be playing for him again."
Jaissle said Dedić would bring "both defensive and attacking qualities" to his squad, adding: "He's athletic, aggressive and technically very good, but also has a lot of potential to develop further."
Sporting director Ross Wilson described Dedić as a "modern full-back" capable of playing on either side and adds that he will "strengthen" the Newcastle squad "straightaway".
Dedic made 95 appearances for Salzburg before loan spells with Wolfsberger AC and Marseille, and joined Benfica permanently last summer.
He featured for Benfica at St James' Park in last season's Champions League and has won 31 caps for Bosnia and Herzegovina, representing his nation at the World Cup.
