The business being sold employs 51,000 people in 67 different call centres, of which 48,000 people and 53 centres are in India.
It is expected to generate revenues of £235 million this year and would have contributed trading profits of some £23 million.
The sale was worth £9 million more than the value of the business on Serco’s books.
Serco said that in its loss-making UK BPO operations it had made some progress in ending unprofitable contracts early, but the rest were still likely to make a loss of £11 million this year.