Runners up in the Bundesliga last season Dortmund sold their star striker Erling Haaland to Manchester City in the close season.
The 34-year-old Frenchman Modeste completed a medical check on Monday and signed a one-year deal with the club, Dortmund said.
More high-profile forwards were considered for the job including Memphis Depay, Mauro Icardi, Edinson Cavani and Luis Suarez, however Dortmund went for Modeste due to his familiarity with the Bundesliga.
Sporting director Sebastian Kehl said Dortmund were happy to be adding a “classic striker” to their squad for the current season.
Kehl described Modeste as a “seasoned professional who knows the Bundesliga very well, who scored 20 goals last season and who, with his profile, can take on exactly the role that our coach Edin Terzic envisages”.
German media reports Dortmund will pay Cologne around five million euros ($5.1 million) for Modeste.
Dortmund were on the lookout for someone to lead the line this season after Haller was ruled out for an indefinite period after being diagnosed last month with a tumour.
He has since had surgery but will be out of action for several months.
Dortmund opened their 2022-23 season with a 1-0 win over Bayer Leverkusen on Saturday.