The offering is being made by some existing shareholders, including investment funds associated with Bain Capital, affiliates of TPG Global, affiliates of 3i Corporation and Temasek Life Sciences.
Quintiles will not receive any proceeds from the sale of the shares in this offering.
Morgan Stanley is acting as the sole underwriter for this offering.
The offering is expected to close on August 5, 2015, subject to customary closing conditions. The company's stock fell about 3% on Friday.