McLaren, who was known as the "voice of rugby" and retired in 2002 after almost 50 years as a broadcaster, died aged 86 in hospital on January 19 last year.
Last week The Bill McLaren Foundation announced plans for the creation of the Bill McLaren Centre of World Rugby in his home town of Hawick in the Scottish Borders.
The theme of the centre will be the story of rugby which will be told, as far as possible, in McLaren's voice.
Scottish Borders Council has agreed to help find a suitable location for the centre as well as offer advice and support.
Councillor Graham Garvie, Scottish Borders Council's executive member for sport, culture and community learning, said: "I am absolutely delighted that this project received full backing from elected members.
"It is a fantastic project and the Bill McLaren Foundation are totally committed to turning their vision into a reality.
"We strongly believe the Bill McLaren Centre of World Rugby will benefit the Scottish Borders economy as well as providing educational opportunities for many young people into the future.
"This is why we will be providing the Bill McLaren Foundation with ongoing support to bring what will be a worldwide attraction to the Borders."
Speaking last week, McLaren's daughter Linda Lawson said: "The centre is a very exciting project, the progress on which has come far faster than we anticipated.
"This is very much a longer-term priority for the foundation and we're indebted to Scottish Borders Council for their help and enthusiasm getting the project thus far already."
The plans for the centre include an interactive educational resource which will give youngsters the opportunity to learn the life skills and techniques that McLaren practised as a teacher, journalist and commentator.
The estimated cost of the project is between 3 million and 4 million, and the foundation said it intended to have the museum up and running within the next three years.
The Bill McLaren Foundation was set up to celebrate the life, achievements and values of the commentator and launched in March last year.
Support for the museum plans were backed at a full council meeting on Thursday.