Reedie was chosen over American former Olympic hurdles champion Edwin Moses and former IOC medical director Patrick Schamasch at the one-day Executive Board meeting in Moscow, an IOC official said.
The 72-year-old sports administrator's new role as head of WADA is expected to be rubber-stamped at the world conference on doping in sport from November 12-15 in Johannesburg.
Reedie, a former head of the International Badminton Federation and the British Olympic Association, has been an IOC member since 1994.
He is also a member of WADA's 12-member Executive Committee and was regarded as a driving force behind London's staging of the Olympic Games last year.
WADA was set up in 1999 by the IOC to fight the growing problem of doping in sport with half its funding coming from the IOC and international federations and the other half from national governments.
The sports bodies and the governments take turns in nominating the WADA president. Current president John Fahey was the governments' choice in 2007.
WADA has recently been criticised for doing too little in the fight against doping while Fahey has said their budget was too small.