The deal, which will see the Belgium international spend the 2017/18 campaign in the Bundesliga, includes a reported loan fee of £6m for the temporary move.
The 22-year-old remains highly rated by the Liverpool management, but the club couldn't provide guarantees over his game time this season, with the player's father even publicly suggesting his son needed to move.
After an impressive World Cup, Origi joined the Reds in 2014, but after a season back on loan with Lille, struggled to earn a regular place in the starting lineup with Roberto Firmino the preferred centre forward under Jurgen Klopp.
The Belgian, who could make his debut for his new side on September 9 at home to Hannover 96, has scored 21 goals in 77 appearances for Liverpool in total.
Liverpool insisted on a clause allowing them to recall Divock Origi from Wolfsburg in January if necessary— paul joyce (@_pauljoyce) August 31, 2017