McCown was scheduled to become an unrestricted free agent.
McCown has played in 16 games, with seven starts, in seven seasons. He has completed 154 of 260 passes for 1,739 yards, with nine touchdowns and 10 interceptions.
The 29-year-old quarterback spent time with Cleveland and Tampa Bay before joining the Jaguars via a trade in September 2009. He was a fourth-round draft pick of the Browns in 2004 and was traded to the Buccaneers in April 2005.
McCown played in one game last season before tearing a knee ligament and missing the rest of the season. He completed 11 of 19 passes for 120 yards in a loss at San Diego.