The Group Chief Executive of the Welsh Rugby Union, Roger Lewis, said: "Gareth's death has shocked us to the core and today's news now dominates all our thoughts.
"Since he went to hospital we have all got to know a lot more about this fine young man and we truly realise how great a loss his death is for everyone who knew him and cared for him.
"Gareth will be remembered as a fine rugby player and, above all, as a loyal and caring human being and a loving and devoted family man.
"Our thoughts and sympathies go out to his close family, friends and all his rugby colleagues at this awful time for them all."
The Chairman of the Welsh Rugby Union, David Pickering, added: "I want to offer my personal condolences to Gareth's family for the terrible loss they have suffered.
"I was at the game when this incident happened and since then I have also been fully aware of how Gareth's friends and family and everyone at Neath RFC have supported each other through this."
Gareth's family have requested that their privacy is fully respected at this difficult time for them all.