Dodds, 21, has penned a two-year deal at Vale Park after the Potteries club paid an undisclosed transfer fee to the Foces.
He scored nine goals on loan for the League Two side Lincoln City last season, and the Vale boss Lee Sinnott believes he is a good addition to his squad.
"He's a player that can operate in the midfield and up front and he has a history of putting the ball in the back of the net," he told BBC Radio Stoke.
"Once he became available, he was a player we were keen to secure his services. We've been aware of him for some time now but it was a case of waiting to get the green light, we're very pleased."