Camille Muffat (25) was killed after her helicopter was involved in a mid-air collision in Argentina.
Mufatt beat Adlington to claim 400m freestlye gold at the 2012 London Olympics to set a new Olympic record.
Paying tribute to her former rival, Adlington said: “So sad and shocked to wake up to hear the tragic death of Camille Muffat. She was an amazing sportswoman, competitor and lovely person.
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“My thoughts go out to not only all her friends and family but to all the family and friends of all the 10 victims. Its an extremely sad day.
“RIP Olympic Champion Camille Muffat. You will be dearly missed. X “
The accident happened after two helicopter scrashed during the filming of TV survival show Dropped.
The crash claimed the lives of nine other people, including fellow Olympian Alexis Vastine and yachtswoman Florence Arthaud.