The 51-year-old Argentine, who is set to return to the Premier League after being sacked by Chelsea's London rivals Spurs in November 2019, will take over from caretaker manager Frank Lampard at the end of this season.
Mauricio Pochettino will permanently succeed Graham Potter, who was dismissed at the start of April after less than seven months in charge.
Despite spending £600m in the last two transfer windows, Chelsea are in the bottom half of the Premier League and will end the season without a trophy, while they will also not play in European competition next season.
Pochettino has been out of work since being sacked by Paris Saint-Germain last summer after 18 months in charge of the French side, having guided them to the Ligue 1 title in 2022 and the French Cup the year before.
The ex-Espanyol boss managed Spurs for five years from May 2014 but failed to win a trophy at the north London club.
He led them to the 2019 Champions League final, which they lost to Liverpool, and also guided them to the 2015 League Cup final and a second-place finish in the 2016/17 Premier League season, with Chelsea winning both competitions.
However, his first trophy came at PSG, where he won the Coupe de France in May 2021 before winning the Ligue 1 title in the subsequent campaign.
Mauricio Pochettino faces a difficult task in restoring Chelsea's fortunes given the club have spent around £600 million since Boehly and Clearlake Capital completed their takeover last May only to sack two managers on the way to a probable finish in the bottom half of the Premier League.
They sit in 11th place with three games to play after Saturday's 2-2 draw at Nottingham Forest.