Corporal William Savage, 30, of Irvine, North Ayrshire, US-born Private Robert Hetherington, 25, who grew up and was educated in Scotland, and Fusilier Samuel Flint, 21, from Blackpool, Lancashire, served with the Royal Regiment of Scotland.
They died after the £1 million Mastiff they were in was blown up by a particularly large and lethal improvised explosive device (IED) planted on the road in Nahr-e Saraj, Helmand Province yesterday.
The three soldiers were airlifted to the main military hospital at Camp Bastion but could not be saved.
Defence Secretary Philip Hammond said they were "exceptional men who served their country with distinction".
It is the first time British soldiers have been killed by an explosion while travelling aboard the 24-tonne troop carrier since it became operational in 2007.
Another six soldiers inside the vehicle at the time are being treated at Birmingham's Queen Elizabeth Hospital, the specialist centre for wounded troops. The Ministry of Defence (MoD) has yet to confirm the seriousness of their injuries.
The deaths take the number of UK service members who have lost their lives since the conflict in Afghanistan began in October 2001 to 444, including six this year.
Cpl Savage – of the regiment's 2nd Battalion, the Royal Highland Fusiliers – had been looking forward to the birth of a son.
In a statement issued via the MoD, his pregnant wife Lyndsey said: "I am completely devastated, but extremely proud of 'Sav' and everything that he has achieved.
"I have lost the love of my life and the father of our son. I know his life will live on through so many amazing memories that we shared together."
The keen sportsman joined the Army shortly after Nato forces invaded Iraq in April 2003. He was deployed once to Iraq and was on his third tour of duty in Afghanistan.
His commanding officer, Lieutenant Colonel Robin Lindsay, said the loss would be a hammer blow to the battalion and the wider regimental family.
Lt Col Lindsay added: "We will remember Corporal William Savage as an exceptional soldier, a dedicated leader and a gentleman in the truest sense of the word.
"He was the classic example of a Scottish infantryman; robust, committed and blessed with a fine line in banter. He had made the battalion proud."
Private Hetherington, of the 51st Highland, 7 Scots, achieved a bachelor of science degree in environmental geography in Scotland after moving from America and represented his adopted country at lacrosse. A music lover, he was described as the "life and soul of the party".
A reservist who had joined the Territorial Army while at university in 2006, he was on his first tour of duty and had hoped to attend the Royal Military Academy at Sandhurst following his debut Afghan deployment. He was expected to excel. The MoD said he was an intelligent and thoughtful soldier who always had a smile on his face.
Lance Corporal Russ MacLean said: "Bobby was my best friend. He was the life and soul of the party and one of the kindest and friendliest people I have ever met. He was always at the end of the phone or across the table at a pub if you had problems you needed to talk about. My heart goes out to his family who will be as distraught as I am.
"He had a loving and caring family, along with his girlfriend Maeve, and my thoughts are completely with them."
Fusilier Flint, 21, also of the Royal Highland Fusiliers, joined the Army in November 2011. He was a Manchester City fan and motorsport enthusiast and, said his family, a "cheeky chappy".
They added: "The whole family is completely devastated. Everyone should know that Sam loved his job and made his whole family and everyone that knew him very proud.
"Sam was always the life and soul of the party, a real ladies' man, witty, funny, the real cheeky chappy. He was a loving son, the protective brother, courageous nephew, the caring uncle, the loyal grandson that anyone would wish to have."
Brigadier Rupert Jones, commander of Task Force Helmand, said: "The loss of these three brave Scottish soldiers comes as a great blow to everyone in the Task Force, but leaves us all the more determined in our task to do justice to their memory."
An investigation is expected to look at how the bomb was made, and how the incident happened – including techniques and checks used by British troops on patrol.
The attack came on the third day of the Taliban's so-called spring offensive. Fighting in 2013 is a key test as the international coalition prepares to hand over security responsibilities to Afghan forces next year.
First Minister Alex Salmond expressed sympathy for the families of the soldiers. He said: "This incident demonstrates once again the dangers faced by our armed forces."