The 19-year-old - who joined the Reds from Celta Vigo in 2021 - broke into the Liverpool first team in the 2022-23 season under Jurgen Klopp, scoring his first goal for the club in a Boxing Day win over Aston Villa.
However, groin and calf injuries restricted Bajcetic to just three senior appearances for Liverpool last term, and he has not been involved in either of their two Premier League victories this season.
With Bajcetic and Liverpool both keen to get him regular game time, the 19-year-old was made available for a temporary spell away from Anfield and was supposedly wanted by Barcelona, who have just lost Marc Bernal to an ACL injury.
Hansi Flick's side were ultimately unsuccessful in their attempts to hijack a deal, though, and Bajcetic will spend the 2024-25 season at Salzburg, who are managed by former Liverpool assistant Pep Lijnders.
The Spaniard's switch to the Austrian powerhouses - known for their stellar development of young players - also sees him link up with Bobby Clark, who left Liverpool earlier this summer to join Salzburg in a permanent deal.
"I am really happy to be playing for FC Red Bull Salzburg. My aim is to help us celebrate lots of successes together. I would like to win the league and impress in the Champions League too with my new team," Bajcetic told the Salzburg website.
"An important reason for my move is that Salzburg have focused on developing young players for many years - it's a club with lots of potential. Pep Lijnders, who I know from Liverpool and value, is the perfect coach for that. I am looking forward to it all!"
Salzburg sporting director Bernhard Seonbuchner also revealed that several other clubs wanted to take Bajcetic on loan for the 2024-25 season, suggesting that Barcelona did indeed make an effort to bring him to Camp Nou.
"We are really pleased about this transfer, also because there were many other clubs who wanted him. It shows how valued we are when it comes to developing talents," Seonbuchner said.
"Stefan is a player who is highly intelligent and can be deployed in lots of different positions. I am certain he will help us and that we will also be good for his development."
Bajcetic to face Champions League heavyweights at Salzburg
Bajcetic's move to Salzburg could see the Spain youth international test his mettle against some of Europe's most feared teams in the Champions League, where Lijnders's side were handed a challenging league phase draw.
Salzburg must take on reigning champions Real Madrid, as well as Paris Saint-Germain, Atletico Madrid, Bundesliga invincibles Bayer Leverkusen and Arne Slot's former team Feyenoord.
Lijnders's men have made a strong start to their domestic campaign, though, sitting top of the Austrian Bundesliga table with a perfect record of nine points from their opening three matches.
Bajcetic could make his debut for Salzburg in Sunday's top-flight trip to Rapid Wien, and he will wear the number eight shirt during his time in Austria, previously donned by Naby Keita.