The 22-year-old, who featured in all four of the Netherlands' Euro 2020 matches, is reported to have cost Dortmund up to €40million.
Malen previously spent time in the academies of Ajax and Arsenal, but it is with PSV that he made his senior breakthrough in February 2018.
He went on to make 116 appearances for the Eredivisie side in all competitions and played a direct part in 79 goals, finding the net 55 times himself and setting up a further 24.
Last season was Malen's best to date in terms of his attacking output as he scored 19 times in 32 Eredivisie games to help PSV finish second to Ajax.
Those 19 goals were scored from 113 shots, 87 of which were not blocked.
Sixty of those efforts found the target, giving him a shooting accuracy of 68.97 per cent – the best return of any player in the Dutch top flight to have had at least 50 attempts.
In February, he became the second youngest player to score 10 or more goals for PSV in three successive league campaigns after Willy van der Kuijlen between 1964 and 1967.
Malen carried that form into Euro 2020, with his four big chances created bettered by only Gareth Bale (five) at the tournament.
𝐃𝐎𝐍e Deal: Malen Announced ✅ pic.twitter.com/TXRRpN4JiZ— Borussia Dortmund (@BlackYellow) July 27, 2021
After being granted permission to train with his new Dortmund team-mates for the first time on Tuesday, BVB confirmed the signing on their official website later in the day.
The forward's arrival will soften the blow of losing Jadon Sancho to Manchester United, at a time when questions persist over Erling Haaland's future at the Westfalenstadion.
However, speaking earlier on Tuesday, Dortmund's head of first team football Sebastian Kehl dismissed suggestions Malen has been brought in to replace Sancho.
"To compare anyone with Jadon is really unfair," he told Sky Sport Germany. "Jadon needed a certain amount of time to develop to that point himself.
"Donyell is a different player. He likes to cut inside from the wing, whereas Jadon liked to stay out wide.
"We have tried bringing in a player with a different profile, and we are very happy with that."