The 12-year-olds and their mother, 43, died after their car collided with an oncoming lorry on the A361 near Barnstaple at 08:25 BST on Monday.
The woman's husband was travelling in a separate vehicle with her 14-year-old son and saw the crash behind them.
The family was from the Milton Keynes area, Devon and Cornwall Police also confirmed.
More on the crash and other news
The woman was pronounced dead at the scene.
Her daughter was pronounced dead on arrival at North Devon District Hospital in Barnstaple, and her son, taken to hospital via air ambulance, died shortly after.
An investigation is under way and police have asked for witnesses to come forward.
A woman and two children were taken to hospital after a crash on the same stretch of the North Devon Link Road on Sunday.
Two children who died in a crash while on holiday in north Devon were twins, police have said.