"It took a man like Francis" to open the grounds to all, museum director Antonio Paolucci said in a statement, describing the gardens as a place "where the splendour of art and the glory of nature combine in an admirable balance".
The luxurious property southeast of Rome, which is larger than Vatican City itself, has breathtaking views of Italy's Lake Albano as well as ornamental gardens and its own farm.
The villa and gardens, owned by the Holy See since 1596, expanded over the centuries to include other properties and now sprawl over 55 hectares (135 acres).
The residence has long been a favourite with popes hoping to escape the infernal heat of a Roman summer, but Francis, known for his simple tastes, has yet to stay there, to the dismay of villagers used to welcoming visiting pontiffs.
The visit may be out of reach for some tourists, however, with guided tours costing €26 for individuals and €450 for groups of up to 15.