The 19-year-old swaps Anfield for Austria after a three-year spell at Liverpool, who poached him from the Newcastle United academy in the summer of 2021.
Clark quickly found his feet on Merseyside and became a prolific goalscorer at youth level, eventually catching Jurgen Klopp's eye and making his first-team Liverpool debut in their 9-0 crushing of Bournemouth in August 2022.
The midfielder also came off the bench in the 2023-24 EFL Cup final triumph over Chelsea, before scoring his first Reds goal in a 6-1 Europa League battering of Sparta Prague later that season.
In total, Clark made 14 senior appearances for Liverpool - scoring one goal and providing two assists - and Arne Slot's side will reportedly receive up to £10m through the sale of the teenager.
The Reds are also understood to have negotiated a 17.5% sell-on clause, and they will also have first refusal to re-sign Clark if Salzburg do decide to sell him further down the line.
The 19-year-old has signed a long-term contract with Salzburg until the summer of 2029 and reunites with Pep Lijnders, who left his role as Liverpool assistant to take charge of the Austrian giants at the end of last season.
Clark hails Sadio Mane, Dominik Szoboszlai inspiration in Salzburg move
Speaking to the official Salzburg website after his signing was confirmed, Clark touched on the growth of former teammates Sadio Mane and Dominik Szoboszlai at Salzburg, renowned for their development of young talents.
"I am pleased to be taking this step in my career, and I can hardly wait to get out onto the pitch with my new team-mates. It is the perfect move to the perfect club for me," the England Under-20 international said.
"I saw at Liverpool the kind of players that are developed in Salzburg like Sadio Mane and Dominik Szoboszlai, and they were a big inspiration for me.
"Everyone knows how great the prospects are for young players here. I also know Pep Lijnders from Liverpool, of course, and the fact he is the coach here influenced my decision."
Meanwhile, sporting director Bernhard Seonbuchner hailed Clark's relationship with Lijnders as a key factor in the £10m transfer, adding: "Bobby Clark is a highly talented player with huge potential, who will improve further with us due to his ability.
"He has developed mostly at Liverpool, has played in the first team there and knows our coach well, as a result. That is definitely a reason we have managed to sign Bobby for FC Red Bull Salzburg."
Salzburg sit top of the Austrian Bundesliga with three wins from three at the start of the new season, and Lijnders's side are also on the verge of reaching the Champions League league phase after beating Dynamo Kiev 2-0 in the first leg of their qualifying playoff on Wednesday.