Allan has joined Atletico Mineiro from Liverpool after failing to make a senior appearance for the European champions.
The 22-year-old has completed a move back to his native Brazil after the Reds accepted a reported fee of £3.2million.
Allan moved to Liverpool from Internacional in 2015 but spent his career at Anfield on loan with other clubs, initially due to work permit issues.
Having played for SJK and Sint-Truiden, he joined Hertha Berlin for the 2016-17 season, making 15 Bundesliga appearances.
Allan played 22 times for Apollon Limassol and then made just four appearances back in Germany with Eintracht Frankfurt.
He enjoyed a more productive loan on his return to Brazil with Fluminense last year.
"Everybody at Liverpool FC wishes Allan all the best for his future career," Liverpool said in a statement.