The 19-year-old midfielder most recently played for Brisbane Roar in the A-League Men and will initially join up with Forest's B team.
"I'm so happy and excited to start this next chapter with Nottingham Forest. I want to thank everyone at the club and my family for supporting me," he told the English Premier League club's website.
"My goals are to train hard and to dedicate myself to being the best I can be, making both my family and the football club proud."
Head of academy Chris McGuane added: "We are delighted to welcome Shae to Nottingham Forest and are excited to see how he integrates into the B team group.
"Shae has had first-team experience out in Australia and is joining the club hungry to improve as a player."
The Liverpool-born Cahill joined the Everton set-up aged 11, featuring in the club's under-18 team before being released last year and heading to Australia to sign for Brisbane Roar.
He made eight appearances, scoring one goal, but left Brisbane by mutual agreement last month.
Forest have also announced the signing of Nikola Milenkovic from Fiorentina for an undisclosed fee.
The Serbia centre-back joins Nuno Espirito Santo's side on a five-year contract after he helped his former club to the Europa Conference League final and an eighth-placed finish in Serie A last season.
The towering defender has been capped 57 times for his country and played every minute of their Euro 2024 campaign.
"He is a key part of our squad planning this summer and I know how enthusiastic he has been to join the club," Forest chief football officer Ross Wilson told the club's website.
"We have long admired his performances with the Serbian national team, and in Serie A and European competitions for Fiorentina."
16°C