Carpenter went 3-for-3 on field goals in last Sunday's 24-3 victory against Jacksonville, including nailing a 53-yarder for the second week in a row.
It continued a great performance down the stretch for Carpenter, who made 16 of his last 17 attempts after starting the season 6-for-10.
Carpenter has one more year left on his contract, and it calls for a $2.675 million base salary.
Kaeding, meanwhile, comes to the Dolphins as the NFL's all-time field goal percentage leader at 87 percent, although his success rate in the playoffs is only 53 percent.
He has been out of the NFL since being released off injured reserve by the San Diego Chargers. Kaeding was 7-for-7 on field goals in three games this season before going on injured reserve because of a groin injury.
It was the second consecutive year Kaeding went on IR. He tore his left ACL on the opening kickoff of the 2011 season on a play where Minnesota's Percy Harvin went all the way for a touchdown.
Kaeding joined the Chargers as a third-round pick in 2004 with one of the draft choices that San Diego got from the New York Giants in the trade that sent first overall selection Eli Manning to the Big Apple.
Kaeding was selected to the Pro Bowl following the 2006 and 2009 seasons. Ironically, he was replaced in the 2010 Pro Bowl game by Carpenter after he had to pull out because of a groin injury.