The 34-year-old has been without a club since leaving West Ham United at the end of last season, when the London club were relegated from the Premier League, and a deal with the Bees is expected to be finalised this week.
Wilson would provide competition for Brazil international Igor Thiago, who Brentford insist is not for sale at any price, despite reports of offers as high as £80m or £90m for the striker this summer. His arrival is also expected to open the door for 19-year-old Belgian forward Kaye Furo to move out on loan for the season.
A proven Premier League operator, Wilson has previously featured for West Ham, Newcastle United and Bournemouth, scoring seven goals in 32 appearances for the Hammers last season despite their struggles.
Across his career in the English top flight, Wilson has scored 95 goals in 271 Premier League appearances. He first made his name at Bournemouth, helping the Cherries to promotion from the Championship in 2014-15 before establishing himself as one of their most reliable finishers, netting 61 goals in 126 top-flight games on the south coast. That form earned him a £20m move to Newcastle United in 2020, where he added a further 47 league goals in 113 appearances before signing for West Ham last summer.
He won nine England caps between 2018 and 2023, scoring twice, and was part of the squad at the 2022 World Cup in Qatar.
Wilson had also been linked with a return to his boyhood club Coventry City, who are preparing for a first season back in the Premier League in 25 years after winning the Championship title last season, as well as previous interest from Everton and Leeds.
Brentford, though, are understood to have moved quickest and most decisively in negotiations, with Wilson keen to remain in the top flight rather than drop into the Championship with West Ham.