The 35-year-old was due to be out of contract at the end of the league year, but the club have chosen to tie him to an extension rather than letting him test the market when it opens in March.
"I know the nature of this business and free agency," Zastudil told the team's website. "I always wanted to be back and I made that known.
"When the Cardinals had a chance to re-sign free agents, I was hoping it'd be me. It's been a great second home for me and I really wanted to come back and play there."
Zastudil had a net punting average of 45.7 yards during the 2013 campaign.