The greenway would create a more traffic free route from Finaghy through the city centre.
Securing the support, Alliance Councillor Tara Brooks said the "possibilities where endless" when it came to delivering on the project.
Tara Brooks expressed that "greenways are magic" as they promote active lifestyles and promote a healthier lifestyle whilst reducing traffic congestion and pollution, giving children safe spaces free of cars.
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In a statement, Tara Brooks said:
"There are great possibilities in Belfast to deliver spaces for all the community to enjoy. The proposed Blackstaff Greenway would provide a way that people could access the Royal hospital and join up to other Greenways to get to the city centre safely on a traffic free route from Finaghy.
"The connection to the train station at Adelaide would connect it to the rail network and to the Lisburn Road. There is an existing link from the Lisburn Road through Adelaide station to the Boucher estate, but it is not attractive – it goes through industrial back lands, is not well used and does not feel safe.
"This Greenway has the potential to expand and link into existing Greenways, promote a modal shift of traffic into the Boucher estate, and provide a much needed respite from the grey industrial landscape."
