The road cyclists were among the Russians banned from competing after a WADA-commissioned report by Canadian lawyer McLaren, found evidence of widespread doping and manipulation of doping tests by Russian athletes and officials.
The trio, Kirill Sveshnikov, Dmitry Strakhov and Dmitry Sokolov, do not appear in the McLaren report, which said that 26 positive doping tests by Russian cyclists had been covered up.
However, to be able to compete in Rio, Russian athletes had to fulfil a series of criteria defined by the International Olympic Committee.
The IOC also called on international sports federations, which ultimately ruled on athletes' participation in the Games, to examine the McLaren report and "carry out an individual analysis of each athlete's anti-doping record".
The Court of Arbitration for Sport (CAS) last year dismissed the three cyclists' appeal against the ban.
"The main task is to prove that the guys are right, that they have never doped and that they were unfairly banned from taking part in the Olympic Games," their coach Alexander Kuznetsov told Reuters, saying the lawsuit's objective was to "clear the athletes' names".
"We are convinced that the result should be in our favour."
In a letter to the International Cycling Union (UCI) in August last year, the IOC said the three cyclists "do not meet the criteria set by the IOC Executive Board" to compete in Rio, according to the CAS ruling on their case.
The IOC said that "nobody implicated" in the McLaren report could be accepted for entry or accredited for the Games, among other criteria.
Kuznetsov said the lawsuit was filed on Monday by Russian lawyers working in Canada, where WADA has its headquarters, but could not confirm to which court.
"As this is a pending case, we are unable to comment at this time," WADA spokeswoman Maggie Durand said.
Sveshnikov declined to comment when contacted by Reuters on Tuesday, saying he was busy training. Strakhov did not immediately reply to a request for reaction via social media. Sokolov could not immediately be reached for comment.
Russia's athletics federation, Paralympic committee and anti-doping agency RUSADA remain suspended over the doping scandals, which have rattled Russian sport in the past two years.
WADA, which is set to audit RUSADA later this month, in June allowed the agency to plan and coordinate testing under the supervision of international experts.