Alex Garrobe was born in Barcelona, Spain. He studied with Jose Tomas, David Russell, William Watters and Josep Pons. He holds the higher Teacher's Degree from the Oscar Esplà Conservatory in Alicante, where he won the Honors Price. In 1990 he was awarded the Alexander von Humboldt Foundation Scholarship to broaden studies at the Musikhochschule in Cologne.
After winning First Price at the 1990 Infanta Cristina Guitar Competition and the 1988 Musical Youths of Spain Competition, the concert career of Àlex Garrobé has quickly developed in Europe, the Middle East, United States and South America. He is also prize winner at the Andrés Segovia Competitions of Almuñecar (1989) and Palma de Mallorca(1987).

He performed in some of the most prestigious international halls, including the Concertgebouw in Amsterdam, Radio France Auditorium in Paris, Auditorio Nacional (Madrid), Lutowslasky Auditorium (Warsaw) XXI Century Auditorium (Beijing). Among his many collaborations as a soloist with orchestra are the performance of concierto de Aranjuez at the Auditorio Nacional (Madrid) in the concert given to Joaquin Rodrigo, and the world premier of the Concert Mare Nostrum of Salvador Brotons performed in the Lublin Guitar Festival (1999, Poland) and conducted by the composer.

He is also frequently invited to take part as jury in some prestigious international competitions, and many composers have written music for him (S. Brotons, S. Iannarelli, M.Smaili, G. Drozd, R.Sogorb..)
He has recorded 4 CDs with labels like Harmonia Mundi, Opera Tres and Columna Music. Two of his CDs are on the Opera Tres label: the complete works of Eduardo Sainz de la Maza, and a second of 20th century British music featuring pieces by Sir Malcolm Arnold, L.Berkeley and S. Dodgson. Sir Malcolm Arnold commended this record as a "Masterly interpretation, so gratifying to listen ones music played so superbly”. The other two cds are on the labels Columna Música and Harmonia Mundi and feature the Concierto Italiano by Ricardo Llorca and the Concerto Mare Nostrum by Salvador Brotons.
Currently he resides in Barcelona where he teaches at Escola Superior de Musica de Catalunya. He is also regularly invited to give master classes in several music institutions and universities: Stockolm, Warsaw, Oslo, Amsterdam, London(Guildhall School), Helsinki(Sibelius Academy ) Peking or Tokyo.