The move includes sell-on and buy-back clauses for City, along with matching rights should another club make an offer for Heskey in the future.
Heskey made his senior debut for Manchester City in the Carabao Cup last season and also scored the winning goal in the FA Youth Cup final as City beat rivals Manchester United to lift the trophy.
Despite that breakthrough, first-team opportunities at the Etihad remained scarce given the strength of City's forward options, prompting the club to sanction a move that sources say will allow him to develop through regular first-team football rather than further loan spells or fringe involvement in the senior squad.
The switch to Cologne continues a pathway that has already seen one City academy graduate move to the club this summer, with centre-back Jahmai Simpson-Pusey completing a permanent transfer last month. Heskey's arrival suggests a deepening relationship between the two clubs when it comes to developing City's most promising young talents in senior European football, with Cologne offering a route to regular Bundesliga minutes that would be far harder to come by in the Premier League at this stage of his career.
Heskey's father Emile made 62 appearances for England, scoring seven goals, and played for clubs including Leicester City, Liverpool, Birmingham City, Wigan Athletic and Aston Villa during a lengthy career at the top of English football.
The structure of the deal, including City's retained sell-on and buy-back rights, reflects the value the Premier League champions continue to place on the teenager's long-term potential even as they sanction his exit for first-team development purposes.
The move reflects a broader trend among Premier League academies of sending promising young talent abroad to gain senior experience rather than risk stunting their development in under-23 or loan football domestically.
For City, retaining sell-on and buy-back rights allows the club to benefit financially or reclaim the player later in his career should he fulfil his potential in Germany, a structure increasingly common in deals involving elite academy graduates. Heskey now joins a growing group of English teenagers making the switch to continental football in search of regular first-team opportunities, with Cologne offering him a clearer route into senior matches than he could currently expect at the Etihad.