The European champions have been chasing the playmaker for several months, while Tottenham also wanted the 20-year-old.
Chelsea were said to have failed in a previous £20m bid for Oscar, but Sky Sports News understands the Blues have succeeded with an improved offer.
A transfer could now be finalised, despite the playmaker's agent having previously claimed a move to Stamford Bridge was looking increasingly uncertain.
Oscar is expected to arrive in the United Kingdom on Tuesday with the Brazilian Olympic team.
The youngster, capped six times for his country, is regarded as one of the best young talents in Brazil.
Pull on a more traditional look with the Chelsea Team Polo. Simple but classic.
The Chelsea Originals T-shirt from adidas. The classic look of the trefoil can't be beat.
Perfect for carrying your soccer gear to the game or to use to go to work or school. Go Chelsea.
The 2013/14 Chelsea long sleeve soccer jersey. The best fans have a long sleeve jersey.
The Chelsea badge poster is a great addition to any fans room. Show you bleed blue.
Petr Cech will be wearing this NEW Keeper jersey in the 2013/14 Premier League campaign. Be bold.
The 2013/14 Chelsea replica soccer jersey. The sure sign you are a fan of the Blues is by wearing the official jersey.
The latest craze in caps is the old school trucker cap. Get you Chelsea Trucker cap today and be on trend.
Get your young Chelsea fan started early with this Chelsea Mini Kit.
Check out the Chelsea 1976 Retro Soccer jersey. Wear these classic looks when you go out.