Hornicek travelled to the Magpies' pre-season camp in Spain over the weekend to complete the move after Newcastle triggered the release clause in his contract.
Although Eddie Howe's side had already recruited 20-year-old Ewen Jaouen from Reims earlier this off-season, the club remained in the market for a proven option capable of challenging for the number one shirt.
"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," the Czech Republic international said.
"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."
Newcastle's interest followed a lengthy period of tracking Hornicek's development, with his displays last season reinforcing their decision.
The Czech goalkeeper recorded seven clean sheets during Braga's run to the Europa League semi-finals, the highest total by any goalkeeper in the competition.
His distribution also stood out domestically. Opta statistics showed Hornicek completed 846 successful passes in the Primeira Liga, the second-most among goalkeepers, while his 75% passing accuracy ranked fourth.
