Liverpool captain Henderson beat runner-up Raheem Sterling and third-place Harry Kane to the men’s award after leading his club to the Champions League, Super Cup and Club World Cup.
Henderson, 29, also played a key role in England’s third-place finish at the Nations League, and was a regular for Gareth Southgate in central midfield as England qualified for Euro 2020.
Bronze won the women’s honour for the second time following her award in 2015, beating Ellen White and Beth Mead in second and third respectively.
The Lyon full-back also won the Champions League in 2019, and played a pivotal role in England’s journey to the World Cup semi-finals as she scooped the Uefa Women’s Player of the Year award in August.
The awards were decided by a vote among England fans.