The former Arsenal trainee, 23, leaves Leeds for a €2m fee.
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The midfielder joined Leeds from Arsenal in the summer of 2020 and made 35 senior appearances for the Whites.
Greenwood spent 2024-25 out on loan at Preston North End, following a season-long loan at Middlesbrough.
With Pogon Szczecin, Greenwood has penned a deal to 2028.