Carl Cavanagh, 45, was helped out of the water after getting into difficulties during a 1.2-mile swim which formed part of the annual Peguera Challenge event.
But he died after going into cardiac arrest on Tora beach, despite the efforts of medical responders to save him.
His parents and wife Lizzie Cavanagh reportedly witnessed the incident and the near hour-long battle to save him on Saturday.
A routine investigation led by a local judge is ongoing, although unconfirmed local reports said he was suffering “symptoms of drowning” when he was pulled out of the water by event organisers.
In an emotional outpouring on social media today, his wife wrote: “My heart is breaking Carl Cavanagh. Where are you? I need you to take my pain away, please.”
Mr Cavanagh, a father of four, was a crew commander for White Watch at Heathrow Airport for more than 20 years.
Close friend and former White Watch colleague Michael Coates, 36, said he had “lost a big brother”.
The former soldier told the Standard: “He was the most incredible, amazing, caring, loving person. The bond with him was closer than anything I ever had in the military. Everyone is just totally heartbroken and in disbelief.”
Mr Coates added: “He was very, very fit. That is why it is such a tragedy. No one is really processing it.”
The event featured triathletes from countries including the UK, Germany, Brazil and Slovakia and is regarded as one of the best end-of-season triathlons in Europe.
A Heathrow spokeswoman said: “Our deepest condolences are with his family and friends at this time.”