Chambers, who finished the season with 48 catches and set franchise rookie records with 883 yards and seven touchdown receptions, beat out San Diego running back LaDainian Tomlinson for the award.
As for Smith, he became the first Dolphins offensive player honored by the NFL this season. Linebacker Zach Thomas twice was named AFC Defensive Player of the Week this season, while punter Matt Turk was honored twice as the Special Teams Player of the Week.
The league also named Chambers NFL Offensive Rookie of the Month for November.
The only other time Smith was honored by the league came when he was named NFL Offensive Player of the Week for his record-breaking performance in last year's overtime playoff victory over Indianapolis.