Run by the National Trust, Dinefwr Park in Llandeilo is the only example of Brown's work in Wales currently open to the public.
He was commissioned to design the gardens in 1775, by then owners George Rice and his wife Cecil, who was the only child of the fabulously wealthy William Talbot of Hensol in Glamorganshire.
The socialite couple wished to emulate Brown's creations they had encountered at the homes of their friends in and around London, where they spent most of their time.
National Trust Carmarthenshire general manager Jacqui Kedward said: "What visitors to Dinefwr now see today is the vision of George and Cecil Rice with Brown's influence.
"Three hundred years on, Brown's influence is ever present and its splendour is something visitors still marvel at. Last year, we had record visitor numbers, many drawn mainly by the beauty of the landscape."
Capability Brown was born in Northumberland in 1716 - although the exact date is unknown - the fifth son of a land agent and a chambermaid.
Aged 16 he began work as a gardener on the Kirkharle Estate which his father managed.
By 1739 he had moved south, and by 1742 his work - as apprentice to another prominent landscape gardener, William Kent - began to gain notoriety.
Between 1750 and his death in 1783, Brown designed the grounds of more than 170 stately homes, including Blenheim Palace, Warwick Castle and parts of Kew Gardens.
He served George III as royal gardener at Hampton Court, and each of his commissions were said to have earned him about Â£500 (equivalent to Â£61,000 in 2016).
Created when Brown was almost 60, Dinefwr Park is typical of his naturalistic style, which drew praise and criticism in almost equal measure.
Dinefwr's neat flowerbeds and tree-lined paths were ripped up in favour of his trademark undulating grasslands extending right to the house, irregular clumps of trees, and lakes created by damming small streams.
Though seemingly George and Cecil Rice were not taken with all of Brown's suggestions, as a deer park garden and Gothic lodge at the entrance, shown in Brown's sketches, never made it into the finished project.
The commemorative tree will be planted by National Trust director general Dame Helen Ghosh, on Friday, and events to mark the anniversary, including tours of Dinefwr Park's Capability Brown walk, will take place this year.
The 300th anniversary of the birth of renowned landscape gardener Lancelot "Capability" Brown is being celebrated with a tree-planting ceremony.