The incident happened in the back garden of a home in Dalgety Bay, Fife, yesterday morning.
Police officers and Scottish Ambulance Service personnel were called to the address at about 8.20am after the boys were found in what is thought to be a fish pond.
The toddlers were taken to hospital in Kirkcaldy where they were pronounced dead.
A police investigation is under way and Police Scotland have said officers are “supporting the family”.
However, the incident is not being treated as suspicious.
The tragedy happened in a quiet, upmarket cul-de-sac.
Last night, the four-bedroom house was cordoned off with police tape and uniformed officers standing guard.
One neighbour, who did not wish to be named, said everyone was “shell shocked” by the tragedy.
She said she did not know the family.
The neighbour, who has lived on the street for 13 years, said: “It is an awful accident. It is absolutely tragic.
“I feel utterly heartbroken and so very sorry for the family.”
The back garden is not visible from the street but can be accessed via a gate which was last night being guarded by a police officer.
Locals confirmed that there was a pond in the back garden.
A company called Okayama Koi Ltd is listed as having its correspondence address at the property, according to Companies House.
The firm’s Facebook page says it is a “supplier of high quality koi from Momotaro koi farm in Japan”.
The ornamental fish are collected by enthusiasts and tend to require large, deep ponds.
David Walker, of the Royal Society For The Prevention Of Accidents, said around five children between the age of two
and six die every year in the UK from drowning in homes and ponds.
He said: “We don’t usually call for things but we feel ponds should be covered over or temporarily removed if there are
Dalgety Bay MSP Alex Rowley said: “This is awful news and
is every parent’s worst nightmare.
“The loss of two young lives from the same family is just heart-breaking.
“My thoughts and prayers, and those of the whole community, are with the family.”
A Police Scotland spokesman said: “We received a call on Saturday following a report of concern for two children at an address in Dalgety Bay, Fife.
“Two male twins, aged two, had reportedly drowned in a fish pond and officers attended with the Scottish Ambulance Service.
“The children were taken to the Victoria Hospital in Kirkcaldy where they sadly died.
“Officers are supporting the family at this time. Inquiries to establish the full circumstances are ongoing.”