Chelsea owner Abramovich has already spent heavily this season
Piazon, 17, cannot join until he turns 18 next January, meaning the transfer window in the same month is the earliest he can complete his move.
The Brazil youth international is "expected to join on a long-term deal", Chelsea said on Friday.
Chelsea have not disclosed the fee but reports have said it could reach £10m.
Yet to play for Sao Paulo, Piazon is currently with the Brazil Under-17 side at the South American Championship in Ecuador, where Brazil have won two and lost one of their opening three group matches.
Piazon has so far scored twice, a winning goal against Venezuela and in Brazil's defeat by Paraguay.
He had been linked with a switch to Juventus before Chelsea made their move.
Blues owner Roman Abramovich has already spent heavily on one Brazilian this season, signing defender David Luiz from Benfica for more than £20m in January, with Spaniard Fernando Torres also arriving at Stamford Bridge, for £50m.
As well as Luiz, midfielder Ramires and defender Alex are the other Brazilians in Chelsea's first-team squad.
Sao Paulo, the club that produced Kaka, have already seen former players succeed in the Premier League, including Juninho at Middlesbrough.
Juliano Belletti was at the Brazilian outfit from 1996 to 2002 before playing for Chelsea from 2007 to 2010.