Earlier in the window, the DR Congo international removed all association with the club from his Instagram account.
Wissa told the club website: “I’m really happy to be here and to sign for one of the biggest clubs in the Premier League.
“I’m very, very excited to put on the black and white shirt. I’ve got dreams, I’ve got faith, and now I will do my best to make it all happen. I can’t wait to get started.”
Newcastle head coach Eddie Howe added: “Yoane is a player who we have admired for some time and we’re delighted to have him on board.
“He brings proven Premier League quality, demonstrated not only by his goalscoring output but also the crucial work he does for the team.
“Yoane will excite our supporters and complement our style of play – he has pace, power and an excellent work rate. He immediately makes us stronger.”
Wissa joined Brentford in 2021 and went on to score 49 goals in 149 appearances for the club.
He is the second striker signed by Newcastle in recent days, after they also brought in club-record signing Nick Woltemade from Stuttgart on a six-year contract.
Wissa is the sixth senior summer arrival at Newcastle, following Woltemade, goalkeeper Aaron Ramsdale, winger Anthony Elanga, midfielder Jacob Ramsey and centre-back Malick Thiaw.
