The decision, which has been condemned by SAVE Britain's Heritage and UN advisory body ICOMOS, means the 1913 structure will become the largest Grade I-listed structure to be demolished since listing began in 1945.
Built 60 years after Isambard Kingdom Brunel's original station for the Great Western Railway company, the much-debated Fourth Arch extension was designed to match the three original structures.
Landowner Network Rail now plans to continue with proposals to replace the span, which has been hidden from view for more than 10 years because of safety concerns, with offices and shops.
A spokesman for EH said: 'Overall, it was felt that the opportunity of improving the capacity and efficiency of the station for passengers justified the loss of this section of the building.'
He added: '[This] agreement is subject to a number of conditions that will improve the Grade I-listed Brunel building and the public realm around it.'
However, Adam Wilkinson of SAVE believes the proposals are based on false premises. He said: 'Network Rail's plans- are based on presumptions that are out of date or irrelevant.
'Restored and adapted, Span Four will reinforce Paddington Station's rightful place as one of the finest railway termini in the world, while providing capacity for the future expansion of network capacity.'