E! News said Norton, 40, finished in 3 hours, 48 minutes and 1 second.
Edwards, 47, reportedly crossed the finish line shortly after Norton, while Alanis Morissette, 35, completed the race in just under 4 hours and 30 minutes.
Meb Keflezighi won the marathon, crossing the finish line in 2 hours, 9 minutes and 15 seconds.
Swim Week Miami Beach 2014 [PHOTOS]