Crusaders coach Scott Robertson said Matera is one of the "premier loose forwards in world rugby.
"He's a skilful and tenacious player with genuine leadership qualities, who has impressed us with his physicality and work ethic. We're really excited about him joining us next season, and sharing his experience with our young loose forward group who are learning their craft."
Crusaders CEO Colin Mansbridge said they are "still working through the finer detail" of the agreeement.
Matera, 27, who has one season left of his deal in the French Top 14, originally eyed a stint in South Africa before they left the tournament for the Pro 14's Rainbow Cup.
"Stade Francais were very understanding and proposed the option to me. To go and play a season in Super Rugby and then return to Paris to finish my contract," Matera told Midi Olympique.
"South Africa was my first choice. The teams were moved to the Rainbow Cup and this competition would have forced me to travel a lot, I dont want to do that. I then moved to my second choice, New Zealand," he added.
New Zealand sides limit the number of overseas players in their squads the Highlanders' Japan back-rower Kazuki Himeno a rare exemption.
Matera, who was briefly suspended last year after tweets deemed to be racist from 2011 and 2013 resurfaced.
The Buenos Aires-based Jaguares were forced to withdraw from Super Rugby last year for financial reasons.