The Reds have negotiated a 17.5% sell-on clause as part of the deal, which is believed to be for an initial fee of around £20m.
Carvalho was signed by Liverpool from Fulham in 2022 for £5m, and as part of the deal, Fulham will receive 20% of the profit from his move to Brentford.
Southampton had also expressed interest in signing Carvalho, but their offer of around £15m was rejected by Liverpool as it fell short of their valuation.
The 21-year-old impressed during Liverpool's pre-season tour of the United States, scoring in wins against Arsenal and Manchester United.
However, with the return of many first-team players after Euro 2024 and the Copa America, his opportunities were likely to be limited.
Carvalho spent last season on loan at RB Leipzig and Hull City, scoring nine goals in 20 games for the latter.
