Pochettino, 51, signed a two-year deal with the option of a further year and will start work on July 1 ahead of the club's preseason tour to the United States.
Sources told ESPN that although the club spoke to a number of candidates after sacking Graham Potter on April 3, Pochettino was identified as their first choice early in the process and has agreed to work closely with co-sporting directors Paul Winstanley and Laurence Stuart.
Although co-controlling owners Todd Boehly and Clearlake Capital executive Behdad Eghbali had final sign-off, the search was led by Winstanley and Stuart, who said in a joint statement: "Mauricio's experience, standards of excellence, leadership qualities and character will serve Chelsea Football Club well as we move forward.
"He is a winning coach, who has worked at the highest levels, in multiple leagues and languages. His ethos, tactical approach and commitment to development all made him the exceptional candidate."
The club also confirmed Pochettino's backroom staff will include longtime assistant manager Jesus Perez, plus first-team coach Miguel D'Agostino, goalkeeping coach Toni Jimenez and his sports scientist son, Sebastiano.
Owners Boehly, Eghbali, Jose E. Feliciano, Mark Walter and Hansjorg Wyss added: "The sporting team conducted a diligent and thoughtful process that the Board is proud of. We are delighted that Mauricio will be joining Chelsea. Mauricio is a world-class coach with an outstanding track record. We are all looking forward to having him on board."
Pochettino is tasked with steadying Chelsea following a torrid season at Stamford Bridge that has seen the dismissal of managers Thomas Tuchel and Potter and ended with the club finish 12th in the Premier League on 44 points -- their lowest finish since 1994.
Pochettino is the third managerial appointment made by co-controlling owner Todd Boehly following the club's takeover last year.
After coach Bruno Salter took charge for one game, club legend Frank Lampard was appointed as caretaker boss until the end of the season following Potter's departure but was unable to improve their fortunes, winning just one of his 11 games in charge and exiting the Champions League at the quarterfinal stage to Real Madrid.
Former Bayern Munich boss Julian Nagelsmann was one of a number of candidates considered by Chelsea for the managerial post. However, ESPN reported that the 35-year-old pulled out of the race after becoming frustrated at the length of the process, while sources told ESPN he was never close to being offered the role.
After sacking Tuchel and appointing Potter within a 24-hour spell last September, the club was determined to follow a more methodical process and initially drew up a list of five to seven names which also included former Spain boss Luis Enrique and Burnley manager Vincent Kompany.
The contenders were gradually whittled down, but sources close to Chelsea have maintained Pochettino was the only candidate with whom they entered into advanced negotiations.
Sources told ESPN that the Argentine coach feels the project at Stamford Bridge suits him because he will be able to build a young team that can play his style of football.
Chelsea face a season without European football for the first time since the 2016-17 campaign, in which they lifted the Premier League title.
Pochettino has been out of work since leaving PSG last year. He was heavily linked with a return to his former club Tottenham after they sacked Antonio Conte, but sources told ESPN he was never formally approached for the role.
Pochettino won a Ligue 1 title as well as the French Cup and French Super Cup during his 18-month tenure at the Paris club.
He also previously led Spurs to the Champions League final in 2019 and guided the North London club to four successive top-four finishes in the Premier League.