The acquisition is further evidence of WPP's desire to position itself as a broad-based marketing services group. Last week, it bought US marketing services company VML.
Sir Martin Sorrell has said on several occasions that these areas are more profitable than traditional advertising.
Earlier this week, WPP reported that in the first five months of the year like-for-like revenues rose just 4%. Sir Martin told shareholders that the group was in line to improve its operating margins to 15% in 2001 and 15.5% in 2002. The longer-term margin target remains 20%.
QCI was acquired by WPP's direct marketing network OgilvyOne. Its clients include Consignia, IBM, Royal Sun Alliance and NCR.
QCI had revenues of £1.8m and assets of £438,000 in the year to December 31 2000.
Shares in WPP rose slightly to 671.5p, having fallen from yesterday's high of 690p.