The 20-year-old has agreed terms with the Blues until 2028 following a successful trial, moving across London after deciding against extending his stay at Spurs.
Black can operate in midfield or at full-back and has represented England at Under-18 and Under-19 level.
He left Tottenham on 30 June without making a senior appearance for the club and had attracted interest from elsewhere before Chelsea secured his signature.
Sheffield United and Portuguese side Academico FC were among those interested in Black, but Chelsea ultimately won the race for the youngster.
The club see considerable potential in the player and moved for him after assessing him during his trial period at Cobham.
Black has already made an impression since joining Chelsea's academy setup.
He made his debut for Chelsea Cobham Next Gen in August, featuring in the 5-4 victory over West Ham. He subsequently found the net against both Arsenal and Fulham before the September international break.
Those performances led to Black being nominated for the Premier League 2 Player of the Month award for September.
His ability to contribute in more than one position has added to his appeal, with Chelsea able to use him either in midfield or further back.
Black's move also represents a significant change of direction after his decision to leave Tottenham in search of a clearer route towards regular football.
Chelsea have now committed to the former Spurs player through 2028 as they continue to develop young talent within their academy system.