Buckingham Palace said Philip, the nation's longest-serving consort, had the procedure for his pre-existing heart condition at St Bartholomew's Hospital in London on Wednesday.
The Palace said the 99-year-old duke will remain in hospital for "treatment, rest and recuperation" for a number of days.
Concern will be heightened for the duke because of his advanced age, with the Duchess of Cornwall saying on Wednesday that Philip was "slightly improving" and adding: "We'll keep our fingers crossed."
The news was announced amid growing tensions within the royal family ahead of the Duke and Duchess of Sussex's controversial televised Oprah interview, with Meghan saying in an extract that she could not be expected to stay silent if The Firm played a part in "perpetuating falsehoods" about her and Harry.
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Philip has been treated for heart problems in the past and in 2011 was rushed to hospital by helicopter from Sandringham after suffering chest pains as the royal family were preparing for Christmas.
In the serious health scare, he was treated for a blocked coronary artery at Papworth Hospital in Cambridgeshire and underwent a minimally invasive procedure of coronary stenting.
St Bartholomew's is home to Barts Heart Centre - Europe's largest specialised cardiovascular service.
Philip was initially admitted to the private King Edward VII's Hospital in central London on February 16 after feeling unwell, before being moved by ambulance to St Bartholomew's on Monday.
He has now spent 16 nights in hospital - his longest ever stay.
Buckingham Palace said in a statement: "The Duke of Edinburgh yesterday underwent a successful procedure for a pre-existing heart condition at St Bartholomew's Hospital.
"His Royal Highness will remain in hospital for treatment, rest and recuperation for a number of days".
Philip was visited in King Edward VII's Hospital on February 20 by his eldest son, the Prince of Wales, who made a 200-mile round trip and stayed for around 30 minutes.
The duke has spent most of lockdown at Windsor Castle with the Queen for their safety, alongside a reduced household of staff dubbed HMS Bubble.
The couple, who have been married for 73 years, received their first Covid-19 jabs in January.