The restaurant and bar will put fruit and vegetables centre stage, serving modern British dishes with Welsh produce.
It will replace Tom Aikens' Tom’s Kitchen site, which opened on 2010 in partnership with Levy UK - but has now closed.
The new opening is the first London project in a decade for Williams, who took over as chef patron at Odette’s in London in 2008, and opened a restaurant at Porth Eirias in Wales in 2015.
In a statement on Somerset House’s website, Williams said: “I’m a firm believer that a piece of fruit or veg should be treated with the same amount of care and respect as a cut of meat or fillet of fish – if not more.
“I’m thrilled to be opening a new restaurant that’s not only in a stunning location, but where fresh, locally sourced produce is the focus and fruit and veg take centre stage.”
The menu will include small plates such as rainbow carrots, hand-dived scallop, sauterne, and pickled mooli, black garlic, raw apple, sage and Cumbrian beef.
Mains will range from grilled cauliflower, golden raison, capers and soft polenta to a selection of salads and fruit-heavy desserts such as bay leaf panna cotta, blackberry, lime curd and poached rhubarb and blood orange trifle.
The space will also feature Somerset House’s only draught beer bar, with bar fronts made from Welsh slate.
The property is also home to the Spring restaurant, which is headed up by chef Skye Gyngell.
Prior to joining Odette’s Williams cooked under Marco Pierre White at The Criterion, Michel Roux at Le Gavroche for three years, and was senior-sous at The Orrery for four years.