The surprise move comes just months after the HLF turned down a similar grant request, casting doubts over the future of the £15 million Hepworth development - a key part of the city's historic waterfront regeneration proposals.
The latest decision will help kick-start the construction of the new gallery, which will be the home to 30 original plasters by Wakefield-born sculptor Barbara Hepworth.
Once complete the building will also house an 'outstanding' collection of 20th century British art, as well as telling the story of Wakefield's artistic and historic heritage during the past 250 years.
Alan Bowness , the son-in-law of Barbara Hepworth and the former director of the Tate Gallery, said: 'It is wonderful news that the Heritage Lottery Fund has agreed to support the Wakefield art gallery project. David Chipperfield's building will provide the perfect home for the collection of original plaster sculptures that the family is giving to Wakefield, Barbara Hepworth's birthplace.
However, Fiona Spiers, regional manager for the HLF, believes the Lottery cash success is only the first step on the ladder for Wakefield Metropolitan District Council - the scheme's backer.
She said: '[The] hard work starts here for the partners to secure the remainder of the funding for this flagship project, which will undoubtedly put Wakefield firmly on the cultural and tourist map of Yorkshire and beyond.'