The eight-time Gold Medal winner at the Chelsea Flower Show was selected to create a riverside garden by a panel at the Hepworth Wakefield.
The design will be modern, romantic, and “embued with overriding naturalism”, reflecting sculptor Barbara Hepworth’s “deep connection to the landscape.”
One of the highlights of the garden, which is around the size of two-and-a-half football pitches, will be a meadow sown with purple moor grass - found in Yorkshire marshes - as well as other more colourful and exotic species.
Mr Stuart-Smith said he was delighted to be chosen: “Public commissions like these are scarce in the UK.
“I am looking forward to working with the gallery to create a beautiful public space in this riverside setting that will be treasured by residents and visitors alike.”
Four shortlisted designs went on display in garden sheds outside the gallery last October.
Chair of The Hepworth Wakefield Trust David Liddiment said they’d had a “wonderful” response from the public and had taken their views into account, including leaving sculptures on display in the garden.
He added: ““We are absolutely thrilled to be working on this project with Tom Stuart-Smith, one of Britain’s top garden designers, to create a new public space for Wakefield which we believe will enhance the experience of visiting The Hepworth and crucially, attract tourism to the city, further boosting the local economy.
“I feel confident that Tom’s designs for the site will create a cohesive and inspiring landscape that will provide a free, year-round attraction for Wakefield.”
It comes as fundraisers announced a £250,000 gift from the Garfield Weston Foundation, one of the world’s largest charitable foundations, towards the £2.2m project.
The Hepworth’s director Simon Wallis said: “Our fundraising campaign for The Hepworth Riverside Gallery Garden is already underway and I’d like to warmly thank the Garfield Weston Foundation for their major gift. Their significant support has got the project off to a really positive start.”
He added: “Gardens and the Yorkshire landscape were a hugely important part of Barbara Hepworth’s creative life and they influenced her sculpture and its settings.
“It’s fitting, therefore, that we create a natural environment that would have inspired her, and that will have a rewarding all year round dialogue with our superb building and art collection.”
There will be beech hedges in the garden, to protect sensitive plants, and large and small trees scattered throughout.
Others on the shortlist for the garden design included Christopher Bradley Hole and Brita von Schoenaich, Cleve West, and Peter Wirtz.
More details about the garden will be released early next year.