The 24-year-old, who made his senior international debut in May, signed for a reported fee of €30.6 million.
"The last few days have been an emotional rollercoaster from when I first heard about the move, and now I'm so happy to be here," Hornicek said in a statement.
"It's a brilliant opportunity in a new league, which I'm very excited about. From the very first moment I arrived here, I received a fantastic welcome and really felt the warmth of the club. Everyone has been brilliant in helping me settle in.
"I know Newcastle is a huge football city, with 52,000 fans at St James' Park creating an incredible atmosphere and pushing the team every game. I can't wait to play in front of them."
Hornicek arrives after a strong campaign with Braga, helping them reach the Europa League semi-finals, keeping seven clean sheets - the most by any goalkeeper in the competition.
He joined Braga on loan from Czech club Pardubice in 2019 before making the move permanent and establishing himself as first-choice goalkeeper in 2025.
Hornicek earned a call-up to the Czech squad for the World Cup in North America but did not feature as they exited in the group stage.