Feely, who had spent the last two seasons with New York, replaces Neil Rackers, the Cardinals kicker since 2003.
Rackers, who missed a critical field goal at the end of regulation in a playoff game last season that Arizona still went on to win in overtime, is an unrestricted free agent.
"When you get to free agency and we have no kickers on the roster, that's an unsettling feeling for the organization," Cardinals coach Ken Whisenhunt said on the team's website (www.azcardinals.com).
"We attempted to sign Neil. We were forced to move on to the next guy when we couldn't get anything done."
Last season Feely converted 30 of 36 field goals and made all 32 extra point attempts.
(Writing by Steve Keating in Toronto; editing by Frank Pingue; To query or comment on this story email firstname.lastname@example.org)