Both centres will open in spring 2011 and create around 120 jobs.
Dobbies director of property Stuart Wright said: "We're absolutely delighted by the decisions and we want to thank everyone involved in the planning applications, which will allow us to bring a new generation of garden centres to customers in central and West Scotland. We're aiming to open our doors to customers in spring 2011 so we can now commence our plans for construction to start on both sites."
Wright added: "We will be investing substantially at both Dobbies Garden Worlds which will create new jobs for the communities in Livingston and Braehead, meaning a boost for the respective local economy for many years to come."
Dobbies says both new centres will be guided by the company's environmental policy, which aims to continually raise the practice of energy conservation, sustainable sourcing and recycling across the business.
The Braehead centre will be next to Ikea, while the new Garden World, Livingston, will be located just off Junction 3 of the M8.
Dobbies plant to expand from 25 to 100 centres by 2018.
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