The baby’s name was announced by Kensington Palace yesterday, two days after the birth on Saturday.
As the Lord Lieutenant, the Lord Provost Donald Wilson is the representative of the Crown in Scotland.
He said: “The birth of a baby is always an exciting and important moment. On behalf of the city, I have written to the Duke and Duchess to warmly congratulate them on the safe arrival of Her Royal Highness Princess Charlotte of Cambridge.”
Souvenirs of the birth are already on sale at the Royal Yacht Britannia shop at Ocean Terminal, while the Royal Collection has produced commemorative plates and special £5 coins are available from banks.
The naming of the royal baby Charlotte Elizabeth Diana will be seen as a tribute to William’s father, mother and grandmother.
Charlotte is likely to be a tribute to the Prince of Wales as it is the feminine form of the name Charles.
And the middle names of the princess obviously recognise her great grandmother the Queen – Elizabeth II – and her grandmother Diana, Princess of Wales.
The name Charlotte had been an early favourite with the bookies, but in the last few days had been pushed into second place by Alice.
William’s uncle, Earl Spencer, tweeted his approval of the names chosen by the Cambridges for their daughter.
He said: “Perfect names. My two-year-old Charlotte Diana will be thrilled at cousinly name-sharing. Is at an age where thinks world revolves around her.”
In choosing to call their daughter Charlotte, the Cambridges have picked a traditional name with royal connections.
Queen Charlotte was the wife of George III, known as the “mad king”, and was a keen botanist who founded the world-renowned Kew Gardens.
Their first daughter was called Charlotte and George IV also gave the name to his only child.
It has featured in Kate’s family as her sister Pippa Middleton has it as her middle name.
The name picked by William and Kate for their daughter is likely to become popular with parents across the country.
At the moment, it is languishing outside the top ten most popular girls’ names for last year, as compiled by the website www.babycentre.co.uk.
Top is Sophia, followed by Emily and then Lily. Charlotte is only 17th in the list.
The baby princess will join a host of famous women with the same name from the 19th-century writer Charlotte Bronte and the Welsh singer Charlotte Church to the actress Charlotte Rampling.
The betting industry is estimated to have paid out £1 million to punters who guessed the name, according to Ladbrokes.