Cookson, who described himself as a "peacemaker rather than a street fighter," added that McQuaid's inability to improve the UCI's image convinced him to join the race.
"In January there were still a lot of issues that we needed to be clear about, I hoped that we could get into a situation where relations and the image of the UCI was improving, but that has not happened," he said.
Jaimie Fuller, chief executive of sportswear manufacturer Skins, a cycling sponsor also involved in the Change Cycling Now group that has been campaigning for a shake-up in the sport's management, welcomed Cookson's decision.
"He's got a terrific track record," Fuller said. "With transparency and integrity, he has done an amazing job" at British Cycling.
McQuaid and Cookson are the only declared candidates so far for the September election.
"The passion I and many others have for cycling cannot hide the fact that our international body, the UCI, remains hugely distracted, continuing to flounder in waves of damaging historical controversies," Cookson added in a statement. "For far too many people, our sport is associated with doping, with decisions that are made behind closed doors and with ceaseless conflicts with important members of the cycling family and other key stakeholders. This situation is deeply damaging for our sport, and it has severely compromised the UCI's ability to develop and communicate some of the good work that is happening across the world."
McQuaid, who has led the UCI for eight years, is seeking a third four-year term despite criticism of his leadership in the Lance Armstrong doping case. Cycling has been battered by doping scandals over the last 15 years and its image was badly tarnished last year when the U.S. Anti-Doping Agency established that Lance Armstrong used systematic doping on his way to his seven consecutive Tour de France victories.
McQuaid and his predecessor Hein Verbruggen have been accused of ignoring the doping culture and accepting money from Armstrong in exchange for turning a blind eye to his team's doping practices. Both denied any wrongdoing.
However, McQuaid is praised for the introduction of the biological passport, which monitors an athlete's blood profile over time to look for signs of cheating.
The 61-year-old Cookson promised to carry out a fully independent investigation into the allegations of corruption. Earlier this year, the UCI disbanded its own independent commission to investigate any alleged involvement of the cycling governing body in the Armstrong case.
"I'm not accusing anyone of corruption, let's be clear about that," Cookson said. "The allegations need to be thoroughly and independently investigated. If I'm elected I'll make sure that happens quickly and effectively," he said. "I hope there is not corruption and I hope there was not any collusion or covering up of things that should not have been covered up. But if we do find something, we'll need to deal with it properly."
Cycling has also been hit by several doping cases this season, most recently when high-profile Italian riders Mauro Santambrogio and Danilo Di Luca tested positive for EPO in connection with the Giro d'Italia.
While the UCI's relationship with World Anti-Doping agency has deteriorated over the past few years, Cookson said he will build new bridges with the organization if he wins.
"Cycling is not the only sport with problems but if we don't have a sport that parents can send their children to with absolute confidence, then we are failing," Cookson said. "If elected I will devote myself to rebuilding relations with WADA and establishing with them a completely independent body to deal with anti-doping in cycling so that no one can doubt that it is being tackled without fear or favor. I will also seek their full co-operation in the independent investigation into the UCI's past."
Cookson has been a member of the UCI management committee since 2009. He has led the British federation for 17 years and been promoted by British media as a suitable candidate to restore cycling's image. Cookson is enjoying the full support of his federation, while McQuaid's bid has been endorsed by the Swiss federation after Cycling Ireland withdrew its backing.
"We need to work for the good of cycling globally, and not protect vested interests, wherever they may lie," he said. "The best way we can achieve this is to be much more open on how we operate and make decisions. In essence, my manifesto will outline how I would build trust in the UCI, and what our vision should be, for the future."