The agreement, announced by both bodies, saw WADA make progress in one of the key behind-the-scenes discussions at its World Conference on Doping in Sport.
Providing little details of the inquiry and its remit, WADA and the International Cycling Union said in a joint statement late Wednesday that they have agreed on "the broad terms under which the UCI will conduct a commission of inquiry into the historical doping problems in cycling."
Cookson told The Associated Press earlier that there was an agreement and banned American cyclist Armstrong would be invited to testify. The agreement followed a private meeting between Cookson and WADA President Johan Fahey at the conference in Johannesburg.
"They (Cookson and Fahey) further agreed that their respective colleagues would co-operate to finalize the detailed terms and conditions of the inquiry to ensure that the procedures and ultimate outcomes would be in line with the fundamental rules and principles of the World Anti-Doping Code," the two bodies said.
Armstrong was banned for life in 2012 and stripped of his seven Tour de France titles for doping. He has suggested in interviews that he'd be willing to talk to the commission in return for a reduction of his ban.
Cookson, who was elected to lead the UCI in late September on promises of confronting the sport's drug-stained past, said his body had no power to reduce Armstrong's ban in return for him telling what he knows, but conceded "there has to be some form of incentive" for some witnesses.
"I wouldn't oppose (what) USADA (The United States Anti-Doping Agency) wanted to do (with Armstrong) but I would be very surprised if it was anything like what Lance Armstrong seems to be saying, that he should be treated exactly the same as those who have previously given evidence," Cookson said.
Any possible leniency for Armstrong from USADA would also have to be weighed against the opinion of WADA and the International Olympic Committee. IOC President Thomas Bach said he opposed any lessening and would be "very uncomfortable" with it.
Cookson said the commission would likely start work in early 2014 and he wanted to finish the inquiry within 12 months.
Meanwhile, concerns over Jamaica and Kenya are still on the WADA agenda at its four-day summit, and the world anti-doping authority's board will examine its report from an audit of Jamaica's drug testing program on Friday.
Jamaica sports minister Natalie Neita-Headley told delegates on Thursday that her government would now give more money to national anti-doping body JADCO after the revelations of a major breakdown in its testing program last year — possibly one of the recommendations from the WADA report, which hasn't been made public yet.
Neita-Headley spoke of the country's "financial difficulties," and USADA said it has been asked for help by its Jamaican counterparts.
WADA has provided a copy of its report into the country's drug testing breakdown to the Jamaican government and anti-doping officials and has asked for their feedback before any findings are announced following Friday's board meeting.
WADA also says it welcomes long-awaited moves this week by the Kenyan government to set up an investigation into allegations of widespread doping in the East African country's high-altitude training bases. Kenyan authorities had promised an investigation over a year ago.
In its main business in Johannesburg, WADA will vote on proposed changes to its anti-doping code on Friday, and is expected to bring in longer bans for serious dopers among other updates. The new code will come into effect on Jan. 1, 2015 and in time for the next Summer Olympics in Rio de Janeiro.
WADA is pushing for a doubling of bans for intentional doping offences from two years to four, ensuring a doping cheat will miss at least one Olympics. That proposal, the most obvious deterrent being considered, appears to have widespread approval.
FIFA backs the move to four-year bans, although chief medical officer Jiri Dvorak said the world football body considered provisions for leniency for players who test positive for "social drugs" like marijuana were also important.
"Yes, we support it (the four-year ban). We endorse it for the severe violations of the anti-doping rules," Dvorak said.
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