The head of the UCI hopes to be re-elected in September and will campaign against the body's vice-president, Frenchman David Lappartient.
Cookson, 65, was criticised last week as part of a report into the culture and governance of British Cycling.
Lappartient, 44, said the UCI needed "real leadership" and a "clear vision".
"I have been made aware of a number of issues that must be urgently addressed if cycling is to remain a credible sport," added Lappartient, who is president of the European Cycling Union and served two terms as president of the French Cycling Federation.
In a statement, Lappartient outlined five "pillars" to his bid, including strengthening UCI governance "to make substantial contribution to the Olympic and Paralympic movement" and "promoting the development of women's cycling".
In addition he vowed to lead a "fight against technological fraud" and stressed the "changing nature of sports betting must be better understood".
Cookson was elected as head of the UCI in 2013, the year in which Lappartient became a vice-president.
In responding to news of Lappartient's challenge, Cookson said his rival had "not set out very much detail in his plan, or any vision he may have beyond his well known personal ambition for the role."
He added: "I strongly believe that my track record of restoring integrity and credibility to the UCI, and developing cycling over the past four years, together with my plans for a final four-year term as president, will be judged favourably by the cycling family."
Culture, Media and Sport select committee chairman Damian Collins said Cookson should not be re-elected because of failings when he was in charge at British Cycling between 1996 and 2013.
A report published last week outlined poor governance at the body, a "culture of fear" within the team and oversight by funding agency UK Sport.
Cookson has previously said he has "nothing to be ashamed or concerned about" regarding his time at British Cycling.
His bid to remain in charge at the UCI will be supported by UK Sport but, unlike in the 2013 elections, the body will not back him financially.
The UCI election takes place on 21 September in Bergen, Norway.
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Britain's Brian Cookson will be challenged for his position as president of cycling's world governing body by one of his deputies.