The Colombia international, who has been in excellent scoring form in 2013-14, will move to Signal Iduna Park at the end of the season after five years in the German capital.
The Schwarzgelben were dumped out of the Champions League on Tuesday by Real Madrid at the quarterfinal stage despite winning 2-0 in the second leg, but confirmation of Ramos' long-rumored arrival on a four-year deal should help ease the pain of European elimination.
BVB sporting director Michael Zorc, who had revealed this week that the club will "certainly sign two strikers" in the summer, lavished praise on the Colombia international, who he believes is perfectly suited to Jurgen Klopp's style of play.
"Adrian Ramos is an excellent footballer and one of the top goalscorers in Germany," he told the club's official website. "He fits perfectly with Borussia Dortmund's requirements."
Ramos has been in fine form this season, netting 16 times in 29 appearances, while his overall record with Hertha Berlin stands at 32 goals from 89 outings.
His impressive numbers this season have led to a recall to the the Colombia squad, with Radamel Falcao's chances of being fit to feature at the World Cup this summer still up in the air because of a knee injury.