The 26-year-old, capped seven times by Germany, will become Leeds' first signing since they clinched promotion to the Premier League.
Nmecha will join Daniel Farke's side on a two-year contract on July 1st.
"Having fought off competition from other Premier League sides for his services, everyone at Leeds United looks forward to welcoming Lukas to Elland Road," a statement from the Yorkshire club said.
Nmecha graduated from Manchester City's academy and made his Premier League debut as a substitute against West Ham in April 2018.
After loan spells with Preston, Wolfsburg, Middlesbrough and Anderlecht, he made a permanent switch to the German club in an £11 million deal in 2021.
Nmecha made 73 appearances and scored 19 goals for Wolfsburg.