The 26-year-old joins for an undisclosed fee after scoring nine goals in 38 appearances last season across all competitions at Burnley, who were relegated to the second-tier Championship.
"We've been aware of Jaidon's journey for a long time and have always admired him from afar," said Brentford head coach Keith Andrews,
"He did really well last season, which is difficult in a team that got relegated."
Anthony made 81 appearances in all competitions for Burnley across two seasons, having initially joined on loan from Bournemouth before completing a permanent move last summer.
Brentford begin their 2026/27 Premier League campaign against Tottenham Hotspur on August 22nd.