The 34 year-old has signed a one-year contract after it was revealed new arrival Sebastien Haller will miss a significant period due to being diagnosed with a testicular tumour last month.
Haller had been signed as the replacement for Erling Haaland, who left for Manchester City earlier in the transfer window.
The former West Ham and Ajax striker underwent surgery in the first stage of his treatment, with Dortmund sporting director Sebastian Kehl confirming Haller would be out "for a few months", but adding further treatment plans were still being discussed.
On Sunday, Kehl confirmed Dortmund had reached an agreement with Cologne for Modeste, although he noted the move remained contingent on a medical being completed and personal terms agreed.
With those formalities complete, the Frenchman is set to lead the line for the eight-time German champions in Haller's absence.
Dortmund's new signing said: "I am very grateful to 1. FC Koln for the wonderful and successful time I had there. However, I have now decided to make a change.
"The offer from BVB has given me a special chance to play in the Champions League at my age and to prove myself at the highest level. I am delighted about this opportunity and I promise that I will give everything for the success of the team and the club."
Modeste has scored 83 goals in 190 Bundesliga games, spending two years at Hoffenheim before moving to Cologne for two spells either side of a short period in China and a brief time in France with Saint-Etienne.
His knowledge of the league and aerial prowess will likely have been key reasons for Dortmund targeting him, with Modeste scoring eight headed goals in the first half of last season, the most by a player in the first half of a Bundesliga season since detailed data collection began in 2004-05.
Dortmund won their first game of the Bundesliga campaign 1-0 against Bayer Leverkusen on Saturday thanks to a Marco Reus goal, but did lose another new attacker Karim Adeyemi to injury in the first half at Signal Iduna Park.