The deal involves the UK and French healthcare businesses of Generale des Eaux where the local management will take control in each case. Its French business, Compagnie Generale de Sante, is the leading private hospital group in France where it is four times the size of its nearest rival.
Its UK operation, General Healthcare Group, is the second-largest private hospital operator in Britain, behind Bupa.
CinVen said it intended to merge General Healthcare with Amicus Healthcare of the UK, which it already owns. The merged group will leapfrog Bupa to become the largest private healthcare operator in the country.
Simon Rowlands, a CinVen director, said: "The European private healthcare market offers significant opportunities for expansion and we will provide the investment backing necessary to take advantage of the increasing market for private healthcare and hospital facilities and resources."
According to CinVen, future volumes in UK private healthcare are expected to grow by at least 3 to 5 per cent per year. In the French market, growth is running at an annual rate of 1.7 per cent.
The UK and French businesses will be run independently by their respective management teams. CinVen said it planned to offer equity stakes to French institutional investors. It plans no new hospitals in the UK, but in France it will spend Fr2.5bn (pounds 255m) over the next five years.
Generale des Eaux announced in April that it was considering two offers for its health businesses. The French group will retain a 20 per cent stake in the Paris-based subsidiary Generale de Sante. The management of the UK and French divisions will have a stake of 10 per cent in their respective businesses.
The CinVen deal is the latest in a series of similar mergers and acquisitions in the rapidly consolidating private healthcare market. Only last month Bupa announced an agreed pounds 77m deal to takeover Goldsborough Healthcare.
That was part of a flurry of nursing home deals which has seen Greenacre, Ashbourne, Apta, Court Cavendish and Quality Care Homes all snapped up by larger groups.
Paul Saper, a consultant at Laing & Buisson, said: "There is overcapacity in the sector and the larger companies are gradually snapping up the smaller ones.''
He said the merger of General Healthcare and Amicus would create a powerful player with more negotiating clout with the big private insurers such as Bupa and PPP. The insurers also tend to prefer larger operators when deciding to which hospitals they will send patients.
General Healthcare has annual sales of around pounds 250m, 6,000 employees and is involved mainly in private acute hospital care and private psychiatric care. The private acute hospital division has 26 hospitals in England with a total of 1,419 beds. In psychiatric care it has 11 hospitals with a combined total of 740 beds.
In France, the CGS business has sales of around pounds 500m and employs 9,000 staff across a network of 98 hospitals and clinics. It has around 8,300 beds and day places.