The UCI in October ratified sanctions recommended by the United States Anti-doping Agency after their investigation concluded Armstrong and his United States Postal Service team ran "the most sophisticated, professionalised and successful doping programme that sport has ever seen".
Allegations of complicity and insider knowledge were levelled at the UCI and its leadership, all of which have been denied.
John Coates, president of the International Council of Arbitration for Sport, assembled the independent commission, which will be chaired by the former Court of Appeal judge Sir Philip Otton.
The third member will be the Australian lawyer Malcolm Holmes QC. The commission will hold a hearing in London between April 9-26 next year. Their report is to be submitted to the UCI by June 1 or soon afterwards.
The terms of reference were drawn up by the commission members, with plans to determine facts, examine evidence and make recommendations.
Questions will include whether the UCI were aware of doping practices at US Postal and if not, why not; whether anti-doping policies and procedures were adequate; and, whether there was evidence of widespread doping which was ignored.
The commission will also look at Armstrong's relationship with the UCI, including whether he made payments to them and whether these were appropriate.
The UCI have admitted they accepted a donation from Armstrong in 2002, but strongly deny it was connected to any cover-up of a positive dope test.
Other subjects for consideration include whether those convicted of doping offences should be able to work in cycling and, if not, how such a measure would be enforced.
Pat McQuaid, the UCI president, said: "The wide-ranging terms of reference demonstrate the commission's determination to review fully the issues contained in the USADA report and I welcome that.
"The commission's report and recommendations are critical to restoring confidence in the sport of cycling and in the UCI as its governing body.
"The appointment of these three eminent figures demonstrates clearly that the UCI wants to get to the bottom of the Lance Armstrong affair and put cycling back on the right track."