The 21-year-old joins from De Graafschap in the Dutch second division, where he still had two years remaining on his contract, meaning Deportivo had to pay a transfer fee to complete the move.
Deportivo have not disclosed the fee, but the transfer is believed to be in the region of €1m, according to figures the player himself revealed in the Netherlands. De Graafschap will retain a percentage of any future sale.
"With his arrival, RC Deportivo adds youth, potential and talent to strengthen our midfield for the coming years," the club said in a statement.
Gijselhart had interest from several clubs, most notably Twente, but Deportivo's promotion proved decisive in swaying his decision. The chance to play in LaLiga, combined with the financial boost the club gains from returning to the top flight, ultimately tipped the balance in Deportivo's favour.
Gijselhart is an orchestrating midfielder known for his defensive awareness, and has progressed significantly this season in particular. He has represented the Netherlands at Under-15 and Under-17 level.
He started 36 of De Graafschap's 38 league matches this season, accumulating 3,060 minutes and providing two assists. His final appearance for the club came in the Eredivisie promotion play-off defeat to Almere City.
Deportivo are expected to add further reinforcements in midfield as they continue building a squad capable of competing in Spain's top division next season.
The signing represents a significant statement of intent from Deportivo as they prepare for life back in LaLiga after their absence from the top flight. Targeting a player with interest from a club the calibre of Twente, rather than settling for a lower-profile addition, suggests the Galician club intend to build a squad capable of more than simply surviving their return to the highest level of Spanish football.
Gijselhart's profile as a young, progressive midfielder with defensive discipline fits a broader trend among newly-promoted Spanish clubs of targeting technically proficient players from smaller European leagues, where value can still be found before a player's stock rises significantly following a breakthrough season.