Olympic heptathlon champion Ennis was on the three-strong final shortlist, but lost out to Felix, who won three gold medals at London 2012, at an IAAF ceremony in Barcelona on Saturday.
Felix, 27, won the 200 metres and the 4x100m and 4x400m titles in the summer.
New Zealand shot putter Valerie Adams had also been in contention.
Usain Bolt won the men's award for the fourth time in the last five years.
He beat Olympic 800m champion David Rudisha and 110m hurdles gold medallist Aries Merritt.
The pair have both set world records this year, while Bolt successfully defended his three sprint titles.