Hayman said: "It's a big step for me to take but at the same time it's a big opportunity.
"Hopefully I will be going to Newcastle as a member of an All Blacks team that wins the World Cup, which is my immediate goal.
"I've had fantastic opportunities already in New Zealand with Otago, the Highlanders and the All Blacks and I'm grateful for the support I've received."
He added: "Going to Newcastle now doesn't mean I'm totally lost to New Zealand rugby - I'd like to think I could come back and round out my career here."
Falcons director of rugby John Fletcher said: "This is a huge statement of intent by the club.
"At the start of the season myself, our chairman Dave Thompson and our forwards coach Peter Walton made a commitment to go out and sign the best tight head in the world, and we've done it.
"It has been a lengthy process, but we felt Carl was worth the wait because he is the calibre of player who can take our team forward and help drive us on to where we aspire to be."