McQuaid said international legal firm Baker & McKenzie confirmed to the governing body that he is entitled to compete against British rival Brian Cookson.
"The nominations are valid. They came in before the closing date (of June 29)," McQuaid told reporters at UCI headquarters.
Lawyers for Cookson, the British Cycling president, have questioned whether McQuaid's candidacy meets UCI rules ahead of the September 27 poll.
Cookson also raised concern that UCI staff may have breached protocol by helping Malaysian officials draft a rule amendment allowing any two member countries to propose a candidate, and to apply it retrospectively for the current contest.
The proposal, which UCI member countries must approve at their election meeting, came in after McQuaid struggled to secure support from his home Irish federation or Switzerland, where he lives.
Cookson has described the UCI staff's intervention as "a bizarre and deeply worrying set of events."
McQuaid said the governing body's legal advisers in Geneva did not agree.
"It clears the UCI completely from any wrongdoing and it clears the UCI administration of any wrongdoing or any favoritism or ... acting improperly in any way," he said.
Asked if Cookson might challenge his candidacy and the UCI's handling of election rules at the Court of Arbitraton for Sport, McQuaid said: "I would hope that we would not be reduced to that."
"If I am beaten I will walk away. I won't be any going to any (legal) process or anything like that," he said.
McQuaid is seeking a third four-year term following widespread attacks on the UCI and its credibility.
Those intensified in the fallout from the Lance Armstrong doping affair and continued revelations of an endemic culture of doping in recent years.
Cookson, who has served under McQuaid on the UCI management board since 2009, has promised to restore cycling's reputation.
The Malaysian rules proposal can be voted on at the September 27 congress in Florence, Italy, before a 42-voter electoral college chooses the president by secret ballot.