The members of Morat have known each other since they were five years old. They started playing together several times and, when they finished their formation, they decided to create a band. Some of their musical influences are Joaquín Sabina, Eric Clapton and Bacilos.
The band's original name was "Malta". The name was inspired by a pet owned by Isaza. They switched to "Morat" because it was the surname of an ancestor of Alejandro Posada, a former member of the band. The name was also inspired by the farm where the band made their first rehearsals which were named "La Morat":
In 2018, Morat released their second studio album the single Balas perdidas. The single "Cuando nadie ve" peaked at No.1 on Billboard on August 18, 2018, and the single "No se va", released on March 7, 2019, hit almost 2 million visits on YouTube in less than a week.
Equipped with this success, Morat kicked off their first-ever US tour titled "Balas perdidas" to promote their album in 2019, with their first performance in San Francisco on April 4, 2019. The tour ended in Orlando on May 5, 2019, with performances in other cities such as Los Angeles, Chicago, and New York
In April 2019, Morat released a song collaborated with Aitana named "Presiento".[14] This single received more than 600,000 streams on Spotify in its first 24 hours. After that period of time, "Presiento" became the song with the highest debut in Spain, with more than 230,000 streams there, beating Rosalía and J Balvin's 2019 track "Con altura". "Presiento" was later included in the re-issue of Balas perdidas, Balas perdidas (Edición especial), on May 10, 2019, together with three other songs.
On December 15, 2019, Morat ended their Spain tour with the last performance at the WiZink Center in Madrid. Antonio José, Aitana, Cali y El Dandee, and Cami were also invited to perform at this concert. Up to this show, Morat has held more than 80 concerts in 13 countries. and in 2023 it meets again in Chicago on February 09th, 2023 at Copernicus Center.