Fowler, 44, takes charge of the A-League club despite limited managerial experience, although he was player-coach of Thai club Muangthong United in 2011-2012 and has worked with the Liverpool academy.
A star forward during his playing career – the former England international was idolised at Anfield and has scored the most Premier League goals for Liverpool – Fowler also enjoyed two seasons in Australia with the North Queensland Fury and Perth Glory.
He will take charge of Brisbane beginning next season, the Roar guaranteed to finish second last in the A-League table with one game to play this campaign.
"I'm really looking forward to the challenge and am determined to bring success to a club that has such a proud history in the Hyundai A-League," Fowler said via a statement. "I'm really keen to get started and make a difference.
"My family and I have already experienced living in Queensland, so I'm really happy to be returning and being part of the Brisbane Roar family."
Roar chief executive David Pourre was happy to welcome Fowler, who won the UEFA Cup, FA Cup and two EFL Cups during his playing career.
"I'd like to take this opportunity to congratulate and welcome Robbie to our proud and successful football club," he said. "BRFC is confident that we have appointed an outstanding person and someone who is hungry to succeed.
"I know our members, supporters, sponsors and fans will be excited for season 2019-2020."
Brisbane are three-time A-League champions, but the last of those titles came in 2014.