London-based law firm Rylands Legal is representing the claimants, which include England's World Cup-winning hooker Steve Thompson, former All Black Carl Hayman and ex-Wales captain Ryan Jones.
Many players in the group of more than 180 professional and semi-professional players have also been diagnosed with chronic traumatic encephalopathy, epilepsy, Parkinson's disease and motor neurone disease.
Rylands said the class action is being issued on behalf of the majority of those players, with the rest taking legal action soon.
Jones, 41 revealed his diagnosis of early onset dementia and probable CTE earlier this month and became the latest high-profile player to join the class-action lawsuit.
Rylands said it was the biggest class action of its kind outside the United States, where the NFL has paid more than $1.3 billion to date to former players who developed dementia or concussion-related problems.
"This claim isn't just about financial compensation," Rylands said in a statement.
"It is also about making the game safer and ensuring current and former players get tested so that if they are suffering a brain injury they can get the clinical help they need.
"We aim to challenge the current perceptions of the governing bodies, to reach a point where they accept the connection between repetitive blows to the head and permanent neurological injury and to take steps to protect players and support those who are injured."
The governing bodies have previously said that they take player safety "very seriously". World Rugby said they had not been issued with a legal claim as of Monday morning.
World Rugby, the RFU and the WRU had earlier said in a statement: "We care deeply about all our players, including former players, and never stand still when it comes to welfare.
"Our strategies to prevent, identify and manage head injuries are driven by a passion to safeguard our players and founded on the latest science, evidence and independent expert guidance."
In December 2020, Rylands issued the same three governing bodies with a letter of claim on behalf of nine players alleging negligence over head injuries during their careers.
The firm also represents a group of rugby league players as part of a separate but similar claim against England's Rugby Football League.
Last month, World Rugby extended its sit-out period for players with concussion symptoms, requiring them to avoid playing for a minimum of 12 days.
The governing body has also announced guidelines limiting full contact training to 15 minutes per week and launched a brain health education campaign for players.