The 35-year-old was already under contract for the 2018 season, which means the new deal keeps him under team control through 2020.
Last season was Lee's first with the Cardinals but his 14th in the NFL.
The punter spent the bulk of his career, 11 seasons, with the San Francisco 49ers while earning three Pro Bowl selections and being selected first-team All-Pro three times. He spent the next two seasons with the Cleveland Browns and Carolina Panthers, with an injury leading to an early end to his 2016.
He fortunately found a home with Arizona, setting a franchise record with 47.3 yards per punt.
It wasn't a perfect season for the veteran, who ranked 35th in the NFL with a 39.7 net in 2017. However, he provided enough consistency to solidify the position for the Cardinals.
With a lot of turnover in the roster from last season, this is a spot the organization won't have to worry about for the next couple of years.