Countryman Gary Hunt, 32, retained the Best High Diver of the Year award after a second successive World Cup success.
Hungary's Katinka Hosszu, 27, who won three Olympic golds, was Best Female Swimmer for a third year in a row.
American Michael Phelps, 31, who retired after Rio with a record 23 Olympic golds, won the men's award.
Phelps' 19-year-old compatriot Katie Ledecky, who won four gold medals in Brazil, took the female Olympic performance award from swimming's world governing body.
Peaty, 21, clocked 57.13 seconds to win gold by more than 1.5 seconds and become Britain's first male Olympic swimming champion for 28 years.
Britain's Adam Peaty won Fina's Olympic Performance of the Year award for his world record-breaking 100m breaststroke final win at Rio 2016.