The architecture superstars will team up with Hopkins Architects to build a 'new generation' of hospitals for the privately funded organisation, Centres of Clinical Excellence.
The practices were chosen from nearly two dozen firms from around the world and will be asked to deliver around 20 new ground-breaking facilities to provide 'elective surgery'.
It is understood Foster and Partners has already been charged with working up a strategic brief for the whole project, which will inform the design for the individual sites.
Centres of Clinical Excellence executive director Rory Coonan, a former Arts Council of England director, said: 'This is a serious attempt to re-engineer healthcare.'
'We have appointed architects who have never done any hospitals before - innovators rather than hospital architects. Firms who have a great history of innovation. We want to put the hospitality back into hospital.'
'He added: 'These will not be enormous hospitals, generally two to three storeys, perhaps about 5,000 sq m.
'They will work with clinicians on what the expectations of a hospital should be.'
Speaking about the ambitious plans, Richard Rogers said: 'There is a long history linking attractive buildings and space with healing.
'Hospitals which are well designed and integrated into the communities they serve should be celebrated through distinctive architecture.'