The Panthers gave the Dolphins a draft pick in return. McCown became expendable in Miami after the Dolphins brought in Chad Pennington.
The move gives the Panthers a backup quarterback with some experience behind starter Jake Delhomme. Reserve Matt Moore suffered a bruised shin in Thursday's preseason game at Pittsburgh. Hurney said Moore is day-to-day. Brett Basanez, in his second year, was Carolina's only other quarterback.
McCown, 29, previously was with Oakland, Detroit and Arizona and has made 31 career starts. The former third-round pick has thrown 35 touchdowns and 40 interceptions.
"Josh is a guy we've liked for several years," Hurney said. "We attempted to sign him when he was a free agent. We feel like he adds depth to our quarterback situation."
The Panthers have until Saturday to clear a roster spot for McCown, meaning the team will have to trim its roster by 22 players to reach the regular-season limit of 53 plus receiver Steve Smith, who will be placed on the reserve-suspended list. With the Panthers unlikely to carry four quarterbacks, the move likely means Basanez will be either released or traded.
McCown could serve as Jake Delhomme's backup if Moore is unable to play in the season opener Sept. 7 at Arizona. Moore bruised his left leg when he was sacked late in the third quarter Thursday night in a preseason loss to Pittsburgh.
Pat Yasinskas covers the NFL for ESPN.com. The Associated Press contributed to this report.