The money will help pay for works on the greenspace surrounding the 19th century water-mill, including installation of London’s first "Archimedes screw" – a cutting-edge hydroelectric turbine in the river Wandle.
The £2.5m project will see parts of the 125-acre estate open for the first time in 130 years, as the Trust looks to convert the site into a world-leading environmental park and tourist attraction.
The centre will look to provide inspiration for sustainable revolution, featuring technology that can be used by homeowners to spearhead their fight against climate change.
HLF chief Sue Bowers said: "This innovative and exemplary approach to restoration, conservation and interpretation will make this a genuinely sustainable ‘deep green’ heritage project that will simultaneously bring alive the industry of the past whilst embracing that of the future."
National Trust’s Thames regional director, Patrick Begg, added: "This is a fantastically exciting time for Morden Hall Park, the National Trust and for me personally.
"We in the Trust all share a passion for Morden, its heritage and for the wider environment in London. This grant allows us to forge ahead with what will be an exemplar for the trust in terms of carbon neutral building renovation."
The park’s water wheel will be fully renovated and conserved while the stable yard will be opened for the first time in a century.
It is hoped the renovated wheel will be used to illustrate the industrial and cultural heritage of the Wandle, while the new hydroelectric turbine stands as an example of the latest in sustainable technology.
New facilities in the renovated stable yard building will include an exhibition centre, workshop space for craft artists, a small cafe and family picnic area.