Villa had already announced a deal had been agreed with the Belgian side, but they were only able to finally present him at their training base on Tuesday, the forward having been given clearance to work in England.
Wesley spent three and a half years in Brugge, becoming a key player over the past two campaigns as he scored 24 league goals in 76 matches.
Said to have cost Villa £22m, Wesley has become the club's most expensive signing, surpassing the £19m ($24m) they reportedly parted with to sign Darren Bent from Sunderland during the 2010-11 season.
Speaking to the club’s official website, Wesley said: “I’m really happy to sign for Aston Villa.
“I was very happy when I heard that Aston Villa were interested in me – and for a record fee.
“I’m just hoping that now I’ll be able to show why out on the pitch. I’m hoping to prove myself on the pitch.
“For me the Premier League is a real stage – a great division. I’m hoping I can adapt quickly and show what I’ve got to offer.
“You’re going to see a lot of power and a lot of quality. I’m really happy to have the chance to play in the Premier League and I’m hoping to play well and score lots of goals.
“I hope to help Aston Villa as best as I can.”
The striker becomes the first-ever Brazilian to don a Villa shirt and will join the club on their pre-season tour of USA next week.
He arrives in the Midlands having spent the past three-and-a-half years in Belgium with Club Brugge, where he won two Belgian First Division titles and two Belgian Super Cups.
Wesley was also awarded the Belgian Young Footballer of the Year for his performances during the 2017/18 season, in which he scored 13 goals in 44 appearances across all competitions.
Prior to joining Brugge, the 22-year-old appeared for Slovakian side AS Trencin where he scored eight goals in 22 games.