The 26-year-old, who has signed a one-year contract with the club, could be involved in Tuesday's pre-season friendly against Derby County.
"I'm over the moon, I'm just glad something could be done, it was in the process for a long time but these football deals tend to go on forever, which in the back of your mind you're thinking is it going to happen?" he told the club's official website.
"I think Vale's style of play suits me and I understand the management, when I joined it was a great place to grow as a player and turn a boy into a man.
"The attraction I got from the supporters as well was fantastic, you have to do the work on the pitch to get respect and that doesn't just come in the first year, I had to keep chipping away in training."
Griffith, who initially departed Vale in 2012, also spent the second part of last season on loan with Micky Adams's team.