First Minister Alex Salmond led Scotland's congratulations to the Duke and Duchess of Cambridge on the birth of their baby son.
The new prince was born at 16:24, weighing 8lb 6oz.
Mr Salmond said: "I am sure that people across Scotland will be absolutely thrilled to hear the news of the birth of a baby boy to the royal couple."
He added: "And they will want to join me in wishing the proud parents many congratulations."
The royal baby was born at St Mary's Hospital in Paddington, west London.
Scotland Secretary Michael Moore said he was delighted to hear that the royal couple, known as the Earl and Countess of Strathearn in Scotland, had welcomed a healthy baby boy.
"The birth of an heir is a significant event for our country and the excitement and warmth on display has shown how much it matters to people across the UK.
"The arrival of a first child is a happy event in any parent's life and I, along with many others in Scotland and across the UK, was delighted to hear the new baby is healthy and well. I wish the new family all the best for the future."
Scottish Conservative leader Ruth Davidson said: "It's thrilling the whole country can welcome this future king into the world.
"Becoming a new parent is a hugely exciting - and daunting - time for anyone and I'm sure Kate and William will be buoyed by the good wishes they receive from all over the world as they look to bring their son home and start family life together."
Anas Sarwar, deputy leader of Scottish Labour, said: "Our congratulations go to the proud parents who must be delighted this moment has finally come and they have our best wishes on this happy day.
"The extraordinary scenes outside the hospital and the palace are testament to the joy felt all around the world for the new arrival and a fresh chapter begins in our country's future."
The Church of Scotland said: "The birth of a baby is a special event in any couple's life and a true gift from God."
Lord Provost and Lord-Lieutenant of Aberdeen George Adam said: "I am absolutely thrilled to hear the happy news and glad to know that the Duchess of Cambridge and the baby are doing well.
"I am sure their royal highnesses will make wonderful parents and hope that they will be given time and the privacy to enjoy this very special time together as a family."