The couple have been isolating at Highgrove House in Gloucestershire, although the duchess, 73, is currently at her Wiltshire home, Ray Mill House.
A friend said she seemed "very happy" after having the jab.
In December, the prince told frontline workers at the Gloucestershire Royal Hospital that he was "way down the list" to be inoculated.
He told staff: "I think I'll have to wait for the AstraZeneca one before it gets to my turn. I'm some way down the list and will have to wait."
His words came as a boost to the Government's efforts to encourage broad uptake of the drug in the face of "anti-vax" campaigners.
But his comments also came amid speculation that he may not want to take the Pfizer/BioNTech vaccine due to his longstanding scepticism of genetically modified products.
Given the green light by the Medicines and Healthcare Products Regulatory Agency in December, the drug is a new-generation "mRNA" vaccine where genetic information is injected into the body that reprogrammes cells to manufacture part of the Covid-19 protein, which then triggers the building of an immune response capable of fighting off the virus.
It also uses nano-technology.
In 2004, the prince was criticised for saying it would be "surprising" if the technology did not "offer similar upsets" to thalidomide.
Both the heir to the throne and his elder son, the Duke of Cambridge, contracted coronavirus during the first wave of the pandemic.
The prince only suffered mild symptoms and lost his sense of taste and smell for a period, while the duke was hit "pretty hard" by the virus and was "very ill."
News of the royal vaccinations comes after Matt Hancock, the health secretary, urged anyone over the age of 70 who has not yet been offered a Covid jab to contact the NHS and arrange an appointment.
Prime Minister Boris Johnson has set a target for all those in four priority groups, including all those over 70, health and social care workers, elderly care home residents, their carers and people deemed to be clinically extremely vulnerable, to be offered a vaccine by February 15.
As healthy 72 and 73-year-olds, the Prince and the Duchess fell into the Joint Committee on Vaccination and Immunisation's fourth priority category, comprising those aged 70 to 74 and people who are clinically extremely vulnerable.
Last month, it was confirmed that the Queen, 94, and the Duke of Edinburgh, 99, had received their vaccinations, administered by a Household doctor at Windsor Castle.
There had been increasing speculation about whether or not the couple had received the vaccine and whether they would make it public, in order to encourage others to do the same.
The decision to let it be known they had been given the jab was made personally by the Queen in order to prevent further discussion, sources confirmed. The royals' medical matters usually remain strictly private.
It has been reported that the NHS wanted "sensible" celebrities and the royal family to promote the jab to combat scepticism over vaccination.
