The family of four were travelling on the A82 north of Fort William on Thursday when they collided with another car heading in the opposite direction.
All four occupants of the first car, which included two young girls under the age of 4, were pronounced dead at the scene.
Police have now confirmed their names as Gemma Cousin (nee Davidson), 26, her husband Rhys Cousin, 25, and their daughters, Peyton, 3, and Heidi, aged one. The family lived in the Inverness area.
A statement has been issued by devastated family members through police.
They said: "Both families are heartbroken by the tragic loss of Gemma, Rhys, Peyton and Heidi.
"They were a young family with so much to look forward to. To have their lives cut short so suddenly and in such circumstances is utterly devastating.
"As a young couple Gemma and Rhys worked really hard to provide a loving, secure and safe home and family life for their girls who they were totally devoted to. They were known by many with both families being extended and their loss will be felt far and wide.
"Due to the horrific circumstances we would like to thank the emergency services and everyone who was involved on the night. We would also like to thank everyone for the support we continue to receive.
"As a family, we now respectfully ask that we are given the time and privacy to grieve and to come to terms with the loss of Rhys, Gemma, Peyton and Heidi."
All four were travelling northbound in a green Mini Cooper car on the A82 at Torlundy when the collision happened around 5.30pm on Thursday.
The other vehicle involved was a red Ford Fiesta car. The 56-year-old woman who was driving suffered serious but non-life threatening injuries.
A thorough police investigation to establish the full circumstances which led to the collision is ongoing.
Anyone who has information or dashcam footage which has not yet been passed to police is asked to come forward, quoting incident 2942 of 20 February.