Cookson was elected in September 2013, succeeding Irishman Pat McQuaid, and will bid to be elected for a second term this September.
Lappartient, the president of the European governing body and a former president of the French federation, on Tuesday announced he will stand against Cookson, who had previously suggested he did not expect to be opposed, particularly by the Frenchman.
The Frenchman's announcement was welcomed by Lance Armstrong, who was stripped of his seven Tour de France titles under McQuaid. Armstrong wrote on Twitter: "ABC (Anybody But Cookson)."
Responding to Lappartient's announcement of his candidature, Cookson said: "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 at the UCI congress in Bergen in September.
"I note that so far David Lappartient has not set out very much detail in his plan or any vision he may have beyond his well known personal ambition for the role. I look forward to debating what matters for the future of cycling over the coming months."
Lappartient, who is a UCI vice-president, said: "I have always voiced my concerns on the various challenges I have witnessed at UCI, and as a vice-president of the organisation, I have been made aware of a number of issues that must be urgently addressed if cycling is to remain a credible sport.
"It is crucial that we have at UCI a president with a real leadership, who is truly engaged and with a clear vision for cycling."
The 44-year-old suggested influencing the Olympic movement was central to his manifesto.
Cookson can already point to tangible success as the International Olympic Committee recently added four medal events to the cycling disciplines - the Madisons on the track and BMX freestyle - to see the sport become the third biggest at Tokyo 2020, after athletics and swimming.
The 65-year-old Lancastrian can also point to successes in the Cycling Independent Reform Commission report into historical performance-enhancing drug use and the establishment of the Cycling Anti-Doping Foundation, which is independent from the UCI.
However, Cookson's detractors may highlight the crises at British Cycling, where he was president for 17 years until 2013, which saw an independent review into the "culture and climate" of the Great Britain team and the ongoing UK Anti-Doping investigation into allegations of wrongdoing in the sport.
Despite those issues, Cookson has the support of British funding agency UK Sport, although he has said he will not be seeking the agency's financial backing in his campaign for re-election.
