The Bundesliga clubs are reported to have paid an initial fee of 30 million euros, with additional performance-related bonuses included in the deal.
The 18-year-old arrives after an impressive season in Belgium, where he registered 11 assists in the top flight. Karetsas has also made a strong start to his international career, scoring three goals in his first 10 appearances for Greece.
Dortmund moved for the attacking midfielder as they look to replace the creativity lost following Julian Brandt's departure on a free transfer.
Speaking after completing the move, Karetsas said he was thrilled to join one of Germany's biggest clubs.
"Borussia Dortmund is a special club and I am incredibly proud to now be able to wear the black and yellow jersey."
Sporting director Ole Book believes the young playmaker has the qualities to make an immediate impact.
"Karetsas will enrich our team with his creativity and intelligence. He is technically very skilled and possesses the ability to find quick solutions in tight spaces, especially in the final third," Book said.
Dortmund continue to strengthen their squad ahead of the new season and have also been linked with teenage Cologne forward Said El Mala.
Last season's Bundesliga runners-up, who finished behind champions Bayern Munich, continue their pre-season preparations with a friendly against Arsenal at the Emirates Stadium in London on Sunday, August 9.
