Reedie, 75, has been involved with WADA since its foundation in 1999 and was elected its third president in 2013.
He had faced stinging criticism from national Olympic committees days before he stood for re-election for WADA's handling of the Russian doping scandal in the build-up to the 2016 Rio Games.
He had to defend the timing of the release of part of the so-called McLaren report into doping in Russia shortly before the August Games.
The report uncovered systematic state-sponsored doping in Russia.
An IOC spokesperson confirmed last week that it had held talks with Reedie about appointing a "neutral" president in future "for the sake of the credibility and good governance of WADA".
Image: WADA president Craig Reedie
Photograph: Reuters