The Nigeria international has joined the Bundesliga on a season-long loan deal after finding playing time hard to come by at the Gtech Community Stadium.
Onyeka started just 11 of his 26 Premier League appearances last season and had to settle for substitute appearances in Brentford's first two matches of the new campaign.
The 26-year-old was given the chance to play 89 minutes in Wednesday's EFL Cup win over Colchester United, but he has now completed a move to the Bundesliga in the hope that he can nail down a regular starting spot in Augsburg's side.
Frank comments on Onyeka's loan departure
Brentford boss Thomas Frank has admitted that the loan move is a "good opportunity" for Onyeka to enjoy regular minutes in one of Europe's top leagues.
"Frank has been an important player during our last three seasons in the Premier League," Frank told the official Brentford website.
"He has been a big part of our success, and I can't praise him enough for that in every aspect. Frank wants to play week in, week out as a starter; this is a good opportunity for him to do that.
"We have a lot of young midfielders who also need minutes, so this is a good loan for Frank and the club."
Onyeka targeting successful campaign
The Brentford man is looking forward to reuniting with Augsburg boss Jess Thorup after previously playing under him during his time at Danish side FC Midtjylland.
Onyeka told Augsburg's official website: "By joining FC Augsburg on loan, I hope to play often and am looking forward to getting to know the team as soon as possible.
@I'm hoping to have a successful season and am looking forward to working together with Jess Thorup again.
Onyeka will not be available for Sunday's Bundesliga away meeting against Europa Conference League participant Heidenheim.
The midfielder will represent Nigeria in the upcoming international break before he links up with his teammates ahead of a home game against newly-promoted St. Pauli on September 15.