The 40-year-old had been in temporary charge of the League One team following Micky Adams's departure on September 18.
Page's spell as caretaker boss saw him win five out of eight matches in all competitions.
"I am really pleased. I had a conversation with the chairman and he has offered me the opportunity to manage the club, which I am very grateful for," he told Vale's official website.
"I think the difference in the approach to games, especially at home, is there for everyone to see and long may it continue.
"This is a proud moment for myself and I would like to thank the fans and players for their support, which will continue to be important in the future."
Port Vale are back in League One action on Saturday when they make the trip to Colchester United.