The 276-year-old Grade 1 listed building was the place where Wesley started preaching and where Methodism began.
Now a visitor attraction, the funding will enable the existing facilities to be updated.
Plans include a new building in the courtyard which will include a cafe, shop and education rooms. While the museum will undergo a makeover, the interior of the chapel won't be changed.
An artist's impression of the side view of the new building.
Revd Ward Jones, Chair of the New Room Trustees and the Bristol Methodist District, said: "We are delighted that the Heritage Lottery Fund has awarded us this significant grant. The New Room has been situated in the heart of Bristol for over 275 years and we now have the chance to look to the future in a very exciting way.
"We will be able to upgrade our current facilities so that we can properly welcome and inform visitors from the local area, from schools and colleges, and from all over the world.
David Worthington, Manager of the New Room, said: "Bristol was the most significant city in John Wesley's ministry and it was at the New Room that he established the template for the Methodist movement that has now become an international Christian denomination.
"We already work in close partnership with Destination Bristol and the new building will provide an even more attractive visitor experience in the heart of the Bristol Shopping Quarter.
The New Room is located in the heart of Bristol city centre, is opens six days a week throughout the year attracting around 25,000 visitors every year. It's hoped the number will double once the new facilities are in place.