At club level, Henderson lifted three trophies during 2019 as the Reds claimed the Champions League, UEFA Super Cup and FIFA Club World Cup.
Liverpool skipper Henderson picked up the men's award ahead of Raheem Sterling and Harry Kane, who were second and third respectively.
Henderson, who won his 50th cap in March, played a key part in England's qualification for Euro 2020 as well as their third-placed finish at the Uefa Nations League.
Bronze, who was also a Champions League victor last term, takes home the gong for a second time after her triumph in 2015, edging out Ellen White, who starred at the women's World Cup, and Beth Mead respectively.
England fans voted for Bronze ahead of 2018 victor Ellen White in second and Beth Mead in third.
Henderson made seven England appearances past year, passing the 50-cap mark during a 5-1 win in Montenegro.
She played in 18 of England's 20 games previous year, highlighted by a superb goal in the World Cup quarterfinal victory over Norway.
Bronze has already won another individual accolade this season, becoming the first English player to win the UEFA Women's Player of the Year after winning a quadruple with Lyon.