The Villains, who secured a return to the Premier League last month in the Championship play-off final against Derby County, will bring the 22-year-old to the Midlands subject to a work permit and international clearance.
He will link up with Dean Smith’s side as they prepare to head to the United States to face Minnesota United in St Paul to kick-off a busy pre-season schedule.
Wesley, who has spent the previous four seasons in the Belgian First Division A, has helped Brugge to two league titles and two Belgian Super Cups during his tenure with them.
He notched up 17 goals across all competitions last campaign, in arguably his best campaign since joining from Slovakian outfit Trencin, helping Brugge to a second-place finish in the Belgian top-flight and a place in the qualifying rounds of the 2019-20 Champions League.
He also scored the winning goal scored against RB Salzburg in the first leg of the last-32 in the Europa League last season, but saw his club bounced by a 4-0 result in the second leg.
The club have also released several big names as they continue to reshape their squad ahead of a top-flight campaign.
Former Australia captain Mile Jedinak leads a host of exits from the Midlands, with Ross McCormack, Glenn Whelan and Micah Richards also among those who will bid the club farewell.
The Villains also seem set to lose on-loan defender Axel Tuanzebe back to Manchester United, as Red Devils boss Ole Gunnar Solskjaer has said he is looking forward to getting a look the centre-back during the club's pre-season.