Some background on the gardens from Vatican City State:
The Vatican Gardens have been a place of quiet and meditation for the popes since 1279 when Nicholas III (Giovanni Gaetano Orsini, 1277-1280) moved his residence back to the Vatican from the Lateran Palace. Within the new walls, which he had built to protect his residence, he planted an orchard (pomerium), a lawn (pratellum) and a garden (viridarium). The event is recorded among other places on a stone plaque which can be viewed in the “Sala dei Capitani” of the “Palazzo dei Conservatori” on Rome’s Capitoline Hill. Created around the hill of Saint Egidio (where the “Palazzetto del Belvedere” is located today) and the courtyards of the Vatican Museums, this was to be the first garden in the Vatican. However, should you visit the Vatican Gardens today you would begin by viewing a totally different area from that first orchard, one located in a more recent addition to what is now Vatican City State. It is there that larger and more recent gardens have been planted, covering together with the original garden about half of the 44 hectares of Vatican City.
And a video of the gardens for your delight.