The Blues reached the finals of both the men’s and women’s Champions League last season, with the men’s side defeating Manchester City to lift the European Cup for the second time - less than five months after Tuchel was appointed manager.
The women’s team were defeated by Barcelona in their first appearance in the Women’s Champions League final but won a domestic treble, sealed by winning the FA Cup with victory over Arsenal at Wembley last month.
Under Hayes, Chelsea also wrapped up the Women’s Super League title and won the League Cup after thrashing Bristol in the final.
Chelsea’s Edouard Mendy also won the men’s goalkeeper of the year award at the ceremony in Zurich.
Tuchel saw off competition from Manchester City manager Pep Guardiola and Italy’s Euro 2020 winning coach Roberto Mancini to win the award for the first time.
Hayes, meanwhile, won the award ahead of England manager Sarina Wiegman and former Barcelona coach Lluís Cortés.
Robert Lewandowski won the award for men’s player of the year for the second season in a row while Alexia Putellas completed a double of individual honours as she added women’s player of the year to her Ballon d’Or success.
Erik Lamela won the Puskas Award for goal of the year after his spectacular rabona goal against Arsenal in the Premier League last season beat competition from Patrick Schick and Mehdi Taremi.
Cristiano Ronaldo, who joined Messi in the FifPro World XI for the 15th consectutive year, also received a special prize for becoming the top goalscorer in men’s internationals.
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