The building at Monklands General Hospital in Airdrie, North Lanarkshire, will be known as the Lanarkshire Beatson.
It is planned as a satellite of the Beatson West of Scotland Cancer Centre in Glasgow. It will use state-of-the-art equipment for patients with lung, breast, prostate and rectal cancers.
Construction is expected to begin at the end of this month, after approval of the finalised plans was granted, and the centre is expected to be up and running by the end of next year. Most of the patients will come from Lanarkshire but patients from other parts of the west of Scotland may also receive treatment on-site.
Janette Fraser, Chairwoman of the West of Scotland Satellite Radiotherapy Project Board, said: "The approval of these detailed plans is the final step in the development process and we are delighted that we now have the green light to create this important new facility.
"As a great deal of work has already been carried out over the last year this could means the new centre could be treating patients in around 18 months time."
Health Secretary Alex Neil said: "This is an important step forward.
"It could mean that more patients in the West of Scotland will be able to access the best possible treatment closer to home."