The 24-year-old, who struggled for opportunities at Vale Park, has joined on a two-year deal and will provide competition for Richard O’Donnell.
The 6ft 3in No 1 featured three times for Vale in the Checkatrade Trophy last term and previously played for Burton.
His arrival follows on from the addition of AFC Sudbury defender Tyler French and Accrington centre-back Ben Richards- Everton, who will officially join when his Stanley deal expires on July 1.
Hornby said: “This is probably the best move I could have asked for.
“I am at the stage of my career where I wanted a move to a big club to really kick on.”
“The supporters here back the club in huge numbers, which is something that really excites me.”
On his latest signing, City chief Gary Bowyer added: “Sam is a great size and will add some real height between the sticks.
“While doing my homework on him, everyone I spoke to told me to sign him immediately.
“At 24, he is at a good age to really progress his career.
“I was encouraged when he said he would not come in to be a No 2.
“He is ready to play games.”