The Magpies beat Chelsea 2-0 at St. James' Park to progress to the last eight for the third straight season, thanks to Alexander Isak's third goal of the campaign and a Axel Disasi own goal.
And they'll now face the Bees on Tyneside in the week commencing 16th December.
Brentford - currently ninth in the Premier League - beat Championship side Sheffield Wednesday on penalties on Tuesday night following a 1-1 draw at the Gtech Community Stadium.
The two sides have met twice before in this competition. The Magpies were 4-1 winners after extra time at the second round stage in 2001-02 - but were beaten 1-0 at the quarter-final stage in 2020-21.
Ticket details will be announced in due course on newcastleunited.com.