The Greece international moves from KRC Genk with immediate effect and has signed a contract until 2031, with Dortmund paying up to €32m including bonuses for the attacking midfielder, in what is reported to be the second-most expensive transfer in the club's history.
Genk have also secured a 10% sell-on clause as part of the deal, with his base salary reported at around €3.5m a year before performance-related bonuses.
Sporting director Ole Book said: "With his creativity and his footballing intelligence, Kos will enrich our team. He is technically very accomplished and has the ability to find quick solutions in tight spaces, especially in the final third."
Karetsas himself said: "Borussia Dortmund is a special club and I am incredibly proud to now be able to wear the black and yellow shirt.
"I'm really looking forward to getting to know my team-mates and soon playing in front of our fans in this impressive stadium. I want to do my part to make sure we're successful together."
Dortmund had made their interest known as far back as the winter window, with the offensive midfielder long regarded as a highly promising talent tracked by the Bundesliga club's scouts for some time. As well as Dortmund, AC Milan, Galatasaray and Paris Saint-Germain were among the clubs interested in the teenager, with negotiations between Dortmund and Genk stretching over more than a week before the two clubs settled on a fee, having initially been some distance apart despite Karetsas already agreeing personal terms.
Karetsas, who was born and raised in Belgium and came through the country's youth set-up before switching his international allegiance to represent his parents' homeland of Greece, made his senior debut for Genk at 16 and went on to record 11 assists in the Belgian top flight last season, second only to Club Brugge's Christos Tzolis, as Genk finished seventh and reached the last 16 of the Europa League, where they were eliminated by eventual runners-up Freiburg. Across all competitions he had a hand in seven goals during that European campaign alone.
He steps into the void left by Julian Brandt, who departed on a free transfer after seven years at the club, and is expected to inherit Brandt's number 10 shirt as he joins up with the squad on their pre-season tour of Japan following his medical. He becomes the latest addition to a busy Dortmund summer that has already included the signings of Joane Gadou, Kauã Prates and Justin Lerma.