The 22-year-old striker spent last season on loan with Belgian side Anderlecht where he scored 21 goals in 41 games across all competitions.
That followed previous loan periods with Bundesliga outfit Wolfsburg along with spells at Championship sides Preston North End and Middlesbrough.
The Hamburg-born centre-forward made his City debut against Leicester in a Carabao Cup quarter-final in 2017.
In total, he has made two first-team appearances for City and also represented both England and Germany at Under-21 level and scored the winner for Germany in the final of the 2021 European Under-21 Championships.
Everyone at City wishes Lukas the very best of luck on his move to Wolfsburg.