The 23-year-old has agreed a four-year deal and will officially become a Light Blues player on July 1.
Sterling spent this season on loan with English Championship club Stoke City, playing 28 games across all competitions.
The former England youth international graduated from the Chelsea academy after ten years in the youth ranks.
Sterling made his debut for the Blues in 2017 but has spent four of the last five seasons out on loan.
The soon-to-be Rangers defender started his loan spells in League One with Coventry City in 2018.
The Englishman joined Wigan Athletic the following season but played ten games before a hamstring strain ruled him out of action for the rest of the campaign.
He also missed 2020-21 due to injuries before moving to Blackpool in 2021-22.
Sterling has grown in leaps and bounds and will be keen to hit the ground running at Rangers.
The Light Blues have already signed Kieran Dowell on a pre-contract deal, with the English midfielder set to join in July from Norwich City.
Manager Michael Beale wants to make quality recruitment this summer, and adding the two Englishmen to his squad will be useful.
Sterling will come in as a much-needed defensive signing, and his versatility to play across the backline will be a huge boost.
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