Roman Abramovich has acted after a dismal start to the season, which has seen the Blues lose the Community Shield to Arsenal and ship five goals in the league.
According to The Sun, Chelsea made Juve an offer they couldn't refuse.
It's unclear how much of the £69m package is straight cash but any of Oscar, Willian and Juan Cuadrado could go in the opposite direction.
But it any case, the fee looks likely to smash the club record of £50m paid to Liverpool for striker Fernando Torres in 2011.
The club remain keen on Everton defender John Stones too.
With the arrival this week of £21m Pedro from Barcelona and Baba Rahman, from Augsburg, on a similar fee, plus £8m keeper Asmir Begovic and striker Radamel Falcao, Abramovich's spending hit a massive £150m in this window.
Pogba, 22, had been lined up by Manchester City and his old club United.
But Chelsea trumped their Prem rivals - and Spanish giants Barcelona - to get a deal done.