The 18-year-old, who has played at international youth level for Australia Under-17s and Under-21s, will join the Whites' academy after signing a two-and-a-half-year professional deal with the Championship side.
A statement from Leeds United read:
“Leeds United are pleased to announce the signing of goalkeeper Robbie Cook, who joins the club from Australian outfit Perth Glory.
“The highly rated and much-sought-after 18-year-old arrives in West Yorkshire after progressing through the ranks with A-League outfit Perth and will now immediately link up with the Academy at Thorp Arch.
“At international level, the shot-stopper has been involved with Australia’s Under-17 and Under-20 sides. Cook has put pen to paper on a two-and-a-half-year professional deal at Elland Road, running until the summer of 2027.
“Everyone at Leeds United would like to welcome Robbie to the club and we look forward to seeing his future development.”
It comes after a trial period in the UK with both Sunderland and Leeds, while other clubs across the top three tiers wanted to sign Cook including United who have been watching the young star for some time now. Leeds sit top of the Championship and with the addition of Cook may have a squad capable of going all the way and lifting the title.