She will be joined by her husband, Vice Admiral Sir Tim Laurence, on her visit to the Scottish capital on Friday (June 3).
Anne will join children for an animal handling session in the Rainforest Room at the zoo, before visiting the penguin enclosure.
She will then visit HMS Albion and inspect a Guard of Honour before boarding the ship.
On the flight deck of the amphibious assault vessel the princess will meet members of the ship’s company and representatives from charities across Scotland supported by the Queen and Anne as patrons, before cutting a commemorative cake.
The Duke and Duchess of Cambridge and the Earl and Countess of Wessex will visit Wales and Northern Ireland respectively.
William and Kate will travel to Cardiff on Saturday to meet some of Wales’s best-known performers before a Platinum Jubilee celebration concert.
They will meet the crew behind the event at Cardiff Castle, learning about the lighting, sound and visual effects for the show before helping with the final preparations.
The couple will also watch rehearsals and meet Aled Jones and Shan Cothi, both hosting the show which will feature Mike Peters from The Alarm, singer Bonnie Tyler, West End star John Owen Jones, drumming weatherman Owain Wyn Evans and the Pendyrus Male Voice Choir.
The performances will finish at 7pm and the crowds can then watch the Platinum Party at the Palace on giant screens in the castle grounds.
Over the extended Jubilee bank holiday weekend the Earl and Countess of Wessex will carry out two engagements in Northern Ireland.
Sophie and Edward will meet children taking part in multicultural street performances, join in with art and craft sessions, and speak to people sharing their personal memories of meeting the Queen.