In 1996, Giedrius Gelgotas completed M. K. Čiurlionis Art Gymnasium (under teacher Jefimijus Taškinas), and in 2003, he graduated from Lithuanian Academy of Music and Theatre (under Prof. Valentinas Gelgotas), where he acquired both his Bachelor's as well as Master's Degrees. In 2002-2003, the musician studied in London (England) under the guidance of one of the most prominent flute professors William Bennett. During the years 2006-2007, Gelgotas studied at University of Music and Performing Arts in Vienna (Austria) under Prof. Barbara Gisler-Haase. Also, the performer has taken part in master-classes in various countries of the world given by such famous professors as Emmanuel Pahud, Wolfgang Schulz, Jeffrey Khaner, Phillipa Davies, Lóránt Kovács, Carsten Husted, Christian Larde, Ian Clarke, Jean-Claude Gerard and Barbara Gisler-Haase.

Giedrius Gelgotas has won the 2nd and the 3rd prizes at the Juozas Pakalnis National Young Performers Competition, the 1st prize at the National Yamaha Competition, and the 2nd prize at the Jurjanu Andrejs International Wind-Instruments Competition (Latvia). The musician was awarded the diploma at the International Rimsky-Korsakov Competition in St. Petersburg (Russia). Moreover, the artist has participated at the Illzach International Chamber Music Competition (France), where together with the Lithuanian Flute Quartet he was awarded the 3rd prize, a special prize for the best performance of a contemporary piece and a special award of the jury. Together with the St. Christopher Quintet Giedrius Gelgotas has won the 1st prize and a special award at the Henri Tomasi International Competition for Woodwind Quintets in Marseille (France).

Giedrius Gelgotas has performed both as a soloist and a member of chamber ensembles in various national festivals in Vilnius, Kaunas, Pažaislis, Biržai, Palanga, and Druskininkai. The musician has taken part in such festivals as Gaida, Sugrįžimai, Baroko kelias, Musica Ficta (Latvia), and FIMU (France). Also, the artist has participated at the international educational music festival Pacific Music Festival (Japan) and the International Bach Academy Stuttgart Festival (Germany).

Giedrius Gelgotas is the member and the founder of the Lithuanian Flute Quartet and the St. Christopher Woodwind Quintet. Together with the quintet the musician recorded a compact disc in 2005. Moreover, in 2006, Gelgotas recorded a sonata for the flute and the piano (with pianist Indrė Baikštytė) for a compact disc by Lithuanian composer Faustas Latėnas. The musician has made numerous recordings for the Lithuanian National Radio, and has played solo with the Lithuanian State Symphony, the Lithuanian Chamber and the St. Christopher orchestras. As a soloist and a member of various chamber ensembles the artist has performed many pieces composed personally for him. Also, as a soloist and a member of various ensembles Giedrius Gelgotas has given concerts in such countries as Japan, Egypt, the USA, Armenia, Spain, Estonia, Finland, Sweden, Denmark, Germany, Austria, Switzerland, Italy, France, Latvia, Russia and etc. The musician has been awarded the letters of gratitude from the Ministry of Education of the Republic of Lithuania and the Municipality of Vilnius City.

Giedrius Gelgotas works at the Lithuanian Opera and Ballet Theatre Orchestra and studies for his PhD at Lithuanian Academy of Music and Theatre. He gives numerous concerts as a soloist as well as with the St. Christopher Quintet, the Lithuanian Flute Quartet, St. Christopher Orchestra and various other chamber music groups. Giedrius Gelgotas is the member of the British Flute Society. Also, currently, the artist is working as a guest solo flutist at the Cairo Opera and Ballet Theatre Symphony Orchestra (Egypt). Moreover, the musician gives flute lessons at the music school Lyra, where one his pupils has already become the laureate of three national competitions.

In 2008, Giedrius Gelgotas is invited to be an assistant at the William Bennett International Summer-School.