The London-based designer has applied for planning permission to build the new Maggie's Centre in the grounds of St James's University Hospital in Leeds, where it will function as a drop-in centre for anyone affected by cancer.
Described as "a collection of stepped planter elements", his design comprises a series of curved structures that each feature rooftops covered in plants and flowers.
The aim is to take advantage of the therapeutic effect of plants, creating a welcoming facility that stands in contrast to the more sterile environment of the adjacent hospital.
A mixture of private and communal meeting spaces will be framed by the structures.
Thomas Heatherwick said the centre will "create a positive environment which will help calm minds and foster a sense of wellbeing".
"Instead of taking away the open space, we wanted to make a whole building out of a garden," said Heatherwick. "The design developed as a collection of large planters defining the building by enclosing a series of shared and private spaces between them."
The Maggie's cancer charity was founded by the late Maggie Keswick Jencks and her husband, architecture theorist Charles Jencks. The first one was built in Edinburgh by architect Richard Murphy to offer support to cancer sufferers, as well as their friends and relatives.
The Heatherwick-designed Maggie's Centre will be constructed next to Bexley Wing, the oncology unit of St James's University Hospital.
Scheduled to open in 2017, it will offer psychological support, benefits advice, nutrition workshops, relaxation and stress management, art therapy, tai chi and yoga.
"Submitting our planning application is an exciting step forward in bringing a Maggie's Centre to Yorkshire," said Maggie's chief executive, Laura Lee.
"A cancer diagnosis and treatment brings with it tough questions and difficult emotions which can leave many feeling isolated," she added. "The programme of support that we will be offering at Maggie's Yorkshire will help to improve the physical and emotional wellbeing of people with cancer across the region."
Heatherwick – whose projects include the controversial Garden Bridge and a recently completed Singapore university building – will also work with landscape designer Marie-Louise Agius of Balston Agius to create a garden around the building.