Designed by Tom Stuart-Smith, the garden will feature outdoor sculptures, public events and a Garden Studio.
The £1.8m garden has been funded by charitable and public donations and will feature four sculptures, including one by Barbara Hepworth.
Works by Lynn Chadwick, Sir Michael Craig-Martin and Rebecca Warren were also installed for the garden’s formal opening on Friday, August 9.
Simon Wallis, Director of The Hepworth Wakefield, said: “It was important to us that the new garden presented both modern and contemporary sculpture to act as an introduction to what first time visitors will find inside the gallery.
"The new garden will allow us to further explore Barbara Hepworth’s legacy and her deep connection to the Yorkshire landscape of her childhood.
“We are delighted to be able to bring to Wakefield art works by such well-known artists for people to enjoy in our new outdoor setting.”
Work is also underway to transform a former Gatehouse, part of the disused Rutland Mills complex, into a catering facility.
Funding for the Gatehouse conversion was provided by the Wilkes Group, founded in 1946 by Gerald Aulton Wilkes, the last owners of the industrial site.
The garden has been created on a previously unused 400,000 square metre strip of land next to the gallery. Once completed in Spring 2020, it will be one of the largest public gardens in the UK.
Rebecca Warren, whose sculpture The Three will be on display in the garden, said: “Visiting the Hepworth for the first time recently I realised what a beautiful museum it is - the large windows to the outside let in loads of natural light.
“The fact that there is a river running around the building was a complete surprise and makes the whole site very special.
“It feels like a rare opportunity to have sculptures in this setting, especially one that is open and free to the public.
“I’m looking forward to seeing my work in this beautiful context and to seeing how it is affected by the changing light of the different seasons.”
It is hoped that the opening of the garden will help encourage more people to get involved in the Yorkshire Sculpture International Festival, which is being held in Leeds and Wakefield this summer.
Public donations, as well as support from a number of bodies including Arts Council England, Wakefield Council and the Morrisons Foundation, have helped to fund the creation of the garden.
Rutland Mills, the historic industrial area close to the Hepworth, is also undergoing a regeneration.
The site is being transformed into a leisure complex with shops, bars and restaurants, after planning permission for the scheme was given last year.
Many of the buildings on site are industrial and have stood empty for 20 years.
Speaking earlier this year, deputy council leader Denise Jeffery said: “This is a major re-development which will have a positive impact by supporting our district’s economy for years to come - by increasing skill levels and creating better jobs to give residents greater opportunities to succeed in the labour market.
“The re-development will transform this historic area of our city into a vibrant, culturally rich environment that we can all be proud of.”
The project, which is being organised by London-based Tileyard Studios, will cost the council £3m and is expected to be completed by the end of 2022.
A number of other regeneration schemes are in place in the area, including the demolition of Chantry House, which is expected to be replaced by houses.
Dame Barbara Hepworth was born in Wakefield in January 1903. She attended Wakefield Girls’ High School and would often travel with her father, a County Surveyor.
Fascinated by art from a young age, she made the decision to become a sculptor at 15 before enrolling at Leeds School of Art, where she met fellow sculptor Henry Moore.
During a career spanning more than 50 years, she travelled the world, studying first in London before travelling to Paris, Florence and Rome.
In a time when female sculptors were rare, Hepworth’s works began as figurative forms, but she later moved onto abstract works.
She has been described as one of the most important artists of the 20th century.
In 1925, she married fellow sculptor John Skeaping. The two welcomed a son, Paul, four years later, and divorced in 1933 after living apart for several years.
She welcomed triplets Simon, Rachel and Sarah with painter Ben Nicholson in 1934.
Following the war, she settled in St Ives, Cornwall, where she worked in Trewyn studios.
In the 1960s, Hepworth became a prolific sculptor, making almost as many works in 10 years as she had in the 35 previous.
She was awarded Dame Commander of the British Empire in 1965, and became the first female trustee of the Tate Gallery in the same year.
In 1974, Barbara Hepworth died in an accidental fire at her studio.