Last week, Clinigen confirmed advanced talks with the private-equity firm over a possible deal. Pressure has built on the company since Elliott Management raised its stake in recent weeks amid reports the activist investor was seeking to break up Clinigen.
Triton has offered 883 pence per share in cash, with shareholders also eligible to receive a previously declared final dividend of 5.46 pence per Clinigen share, the companies said.
"The Clinigen Board believes (Triton's) offer represents an exceptional opportunity for Clinigen shareholders ... We are therefore unanimously recommending it to our shareholders," Chairman Elmar Schnee said in a statement.
Shares of London-listed Clinigen jumped 10% to 900 pence by 0849 GMT, indicating shareholders could be expecting a better proposal. Analysts including Liberum's Alistair Campbell, however, thought a higher counter bid was unlikely.
"Though we do see intrinsic value in the portfolio, a public market turnaround is perhaps not the most expedient way to achieve this, and we see this as a good offer for shareholders," Peel Hunt analysts said in a note.
Private equity buyouts surged 133% to $818 billion globally in the first nine months of the year as investment firms rushed to deploy cash, often paying rich prices to take assets off the public markets.
British supermarket group Morrisons was bought for $10 billion by Clayton, Dubilier & Rice, beating Softbank-owned Fortress Investment Group in a head-to-head auction in October.
Including Wednesday's gains, Clinigen's shares are up about 33% this year.
Clinigen helps drug developers manage clinical supplies and provides real-world data about medicines, and would be the latest addition to Triton's burgeoning healthcare portfolio.
($1 = 0.7549 pounds)
(Reporting by Pushkala Aripaka in Bengaluru; Editing by Sherry Jacob-Phillips, Elaine Hardcastle)
By Pushkala Aripaka