The contract will combine procurement of IT services with the sale of the internal IT division BBC Technology.
BBC chief technology officer John Varney said, "CSC decided to withdraw because during the last few weeks of the negotiations it just felt that it was not the right partner for us."
He said CSC's exit would not weaken the BBC's negotiating hand with the remaining bidders Siemens Business Services and Accenture.
CSC said, "This decision was judged to be in the best interests of both parties."
The withdrawal comes as CSC announced £62m in UK outsourcing contracts with businesses including Allders and Homebase.