The former Tottenham Hotspurs boss has the option to extend the deal for a further twelve months.
Pochettino comes in as a replacement for Graham Potter, who was sacked at the start of April, with Frank Lampard taking interim charge for the rest of the season.
Chelsea finished 12th on the Premier League table despite spending in excess of £600m since Todd Boehly bought the club last summer.
They will be without European football next season.
After stints at Southampton and Spurs, Chelsea will become the third English club Pochettino will manage.
The 51-year-old Argentine had been without a club since leaving Paris Saint Germain last summer.
Pochettino guided Tottenham to the Champions League final in 2019, losing to Liverpool.
He won the Ligue 1 title with PSG in his only full season in charge of the side.
Chelsea's co-sporting directors Laurence Stewart and Paul Winstanley said: "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."
Owners Todd Boehly, Behdad 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."
