The centre will include two linear accelerator (LINAC) bunkers, a cancer assessment unit and administration offices.
It is part of a programme to build up cancer services at the Western General, while development of a new purpose-built Edinburgh Cancer Centre on the site is still underway.
The new centre will link to the existing radiotherapy department and patients will be transferred between the two areas.
It is part of a £20.6 million investment announced in October from the Scottish Government, which will fund a range of oncology construction and refurbishment works, including this centre, improvements to patient accommodation and increasing the number of en-suite single rooms.
The project forms part of a wider masterplan for the Western General Hospital to transform services, create more space, comfort and privacy and provide access to modern facilities and cutting-edge equipment.
Linear accelerators use high-energy x-rays to conform to the shape of a tumour and destroy cancer cells, without destroying the surrounding tissue.
It is the most common method of external beam radiation treatment.
The patient lies on a bed that can be moved into position, while the x-ray beams can also be delivered from many different angles.
Designers HLM Architects said they hoped the building would avoid a “clinical” feel, with warm colour tones and timber accents to reduce patient anxiety.
The LINAC treatment rooms include a ceiling grid in the style of a “bright sky with trees” overhead.
Chris Stirling, site director at Western General Hospital said: “We are delighted to be working with HLM Architects and RMF Health on the new LINAC treatment facility here at the Western General Hospital.
"At a time when patients may feel stressed or anxious, having a treatment space that is bright and welcoming is critical.
"The space will combine architectural and interior design specifically aimed at helping to improve people’s sense of wellbeing with our amazing, dedicated and expert teams who will deliver exceptional patient care.”
Lorraine Robertson, director at HLM, said: “We centred our design approach on creating a space that would support and positively influence both the psychological and physiological health of patients and other building users."