The park owes its name to the renowned Mallorcan poet Miquel Costa i Llobera.

The gardens display many plant and tree species from the desert, subdesert, tropical areas, and highlands.

As well as the collection of species of cacti and succulent plants, the gardens have panoramic views over the city's coastline and port.

The gardens were built under the guidance of the architect Joan Maria Casamor and Joan Pañella Bonastre, professor at the Escuela de Jardinería de Barcelona (Barcelona's Municipal Gardening School) and they were initially used as an outdoor classroom for botany students.

The gardens cannot be seen from the city even though it is just a ten-minute walk from the Columbus Monument, at the lower end of La Rambla.

Among them is a pergola and many sculptures by Catalan artists, such as: Thanks to its convenient location at the foot of the Montjuïc Mountain and next to the sea, temperatures in the middle of the gardens average two or three degrees Celsius higher than those in the rest of the area.