Wissa arrives alongside fellow striker Nick Woltemade as replacements for the outgoing Alexander Isak after a summer of speculation surrounding his future.
The DR Congo international, whose transfer fee was undisclosed by Newcastle, arrives following 49 goals in 149 games for the Bees and bolsters Newcastle's striking options.
Wissa, who will wear the number nine shirt for Newcastle, said, "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's style of play will excite our supporters and complement our style of play - he has pace, power and an excellent work rate. He immediately makes us stronger."
The move comes just days after Wissa's scathing statement against Brentford, where he pleaded with the club to 'keep their word' and allow him to join the Magpies.