The 33-year-old has been at St James' Park since 2018 but has fallen down the pecking order following Nick Pope's summer arrival from Burnley.
Dubravka has now moved to Manchester United as back-up to David De Gea, with United understood to be paying a £2million loan fee.
There is a £6million obligation if the Slovakia international starts a certain number of Premier League games.
Manager Erik ten Hag has been keen to put pressure on De Gea, who made a costly error in Man Utd's 4-0 defeat at Brentford earlier this month.
Man Utd have been tracking a number of other goalkeepers, including Borussia Monchengladbach's Yann Sommer.
Martin Dubravka told manutd.com: "To be joining Manchester United is a special moment in my career and I can't wait to get started, and help the group achieve its ambitions.
"I am joining an excellent group of goalkeepers with lots of experience in the Premier League, and I know that we will push and support each other to keep our standards at the highest levels. The chance to work with David De Gea, alongside Tom Heaton, is one that I am relishing.
"I'd like to sincerely thank everyone at Newcastle United, and especially the fans, for many great experiences over the past four and a half years. I enjoyed every minute of my time there and made amazing memories to look back on. My focus is now on helping Manchester United, and we'll see what the future holds after I have given my all this season. I am excited to be here!"