British media said City had paid a transfer fee of 40 million euros ($41.56 million) for Khusanov, who has played in 13 of Lens' 16 league games this season.
"For such a young defender, Abdukodir is already very intelligent, as well as being strong, aggressive and extremely quick," City said in a statement.
The centre-back is the Premier League's first player from Uzbekistan.
Khusanov joined Lens from Belarusian side Energetik-BGU Minsk in 2023, playing 31 matches for the French team in all competitions.