Kaeding joined the Dolphins on Friday. Carpenter, who went 22-for-27 on field-goal tries this season, first appeared on the injury report Thursday.
Kaeding is the most accurate field-goal kicker in NFL history at 87 percent (180 of 207), and he made the Pro Bowl in 2006 and 2009. He had been a free agent since he was released from injured reserve by the San Diego Chargers on Oct. 30.
He made all seven field-goal tries in three games with the Chargers this year before being sidelined by a groin injury.
"He has demonstrated a record of success as a kicker in this league," coach Joe Philbin said. "He's a hard worker. He's a true professional, and I'm sure he'll do a great job for us."
Copyright 2012 by The Associated Press