The Black Sea Storm have agreed a three-year contract with the player at €2 million per season plus bonuses.
N’Doye still has two-years left on his contract but is expected to leave Hull following their relegation from the Premier League.
The Senegal international was closely linked with a move to Trabzonspor but joined Lokomotiv Moscow instead before joining Hull City last January. N’Doye scored five times in 15 games for the Tigers last season.
Fellow Süper Lig outfit Beşiktaş were also in talks with Hulll over N’Doye but were unable to reach an agreement and negotiations stalled following the Mario Gomez transfer.
The 30-year-old striker had a great record at Copenhagen where he scored 82 times and provided 34 assists in 150 appearances.
Trabzonspor have had a busy transfer window. The Black Sea Storm also recently signed Europa League winner Stephen M’Bia.