The 20-year-old took part his first training session at the Blues' Cobham headquarters on Friday, having finally linked up with his new team-mates after spending the past few weeks on international duty.
A ?25million price tag means big things will be expected of Oscar but he told his new club's official website: "I hope I won't feel any pressure - I am not feeling it at the moment.
"Back in Brazil, when I broke into the national team, people were asking the same question, did I feel pressure at being the number 10 of the team, the new star? But I didn't feel pressure. I think it will be similar here.
"I am coming into a great team but I feel I can cope with it."
Oscar was similarly relaxed about inheriting the number 11 jersey vacated by the iconic Didier Drogba.
"I understand the importance of this number to Chelsea," he added.
"In Brazil, it is the number 10, but here the 11 is a very important number and I just hope that I can do it justice."
Manager Roberto Di Matteo today revealed he was considering throwing Oscar in at the deep end in Sunday's Barclays Premier League opener at Wigan.
Oscar said: "I am really happy that the manager is already thinking of me and putting me in his plans.
"I feel I could do well if I am called upon on Sunday because I have been playing regular games and am in a good rhythm. I am ready to go."
Oscar, who has been taken under the wing of fellow Brazil star David Luiz, added: "I am hoping it will not take too long to adapt.
"There is a multinational team here with other Brazilians and Latin players, not just an English team or league, so they will help me through their past experiences and so I hope it won't be too much of a problem."
Oscar is expected to play in a three-man attacking midfield behind a central striker.
He said: "In Brazil, there is a different type of football, but I think I am seen as an elegant type of ball player, who is creating for other people.
"I may need to change a little bit over here, but I see myself as that sort of a player who can hopefully make a difference to the team."