The quango - which was expected to have concerns over the mixed-use retail and office project - has decided to offer the designs its backing.
EH experts have explained that not only are they unworried by the demolition of an existing building, but they are also impressed by Nouvel's proposed replacement for the One New Change site.
The backing will come as a major boost to developer Land Securities, which is expected to take the project to the Corporation of London's planning committee in December.
An EH statement outlined the official position on the scheme: 'Although the existing building at One New Change provides a neutral backdrop to St Paul's Cathedral, it is neither listed nor within a conservation area,' it says.
'In these circumstances, EH does not wish to object to its demolition.
'We are very encouraged by the replacement scheme designed by Jean Nouvel and believe this has the potential to become an exemplary piece of modern architecture without challenging the prominence of the cathedral.
'The proposals would open up the site with new public routes, create new views of the dome of St Paul's, provide roof-level public access and significantly increase retail floorspace in this part of the city.
'We look forward to taking part in further discussions about the design as it is developed,' the statement adds.