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 match will be played at the SSE Arena in Belfast on Tuesday, 21 November 2017 and will see the Giants play a Colin Shields All Star select.
Glaswegian Shields, 37, first signed for the Giants in 2005 but had brief spells with Sheffield Steelers and the now defunct Newcastle Vipers.
The Great Britain international is Belfast's all-time leading goal scorer.
He has netted 208 goals in 517 games for the Giants.
Shields was selected 195th overall in the 2000 NHL draft by the Philadelphia Flyers and the Team GB regular has won two Elite League titles, the Challenge Cup and Play-offs with Belfast.
Last season Shields was named by the Elite League as the Best British Player thanks to 29 goals and 27 assists in 67 games played.
"Colin has played a part of some of the most famous moments in Giants history, including the 2010 Playoff championship as well as the Elite League titles in 2006 and 2014," said Steve Thornton, Head of Hockey Operations at the Belfast Giants.
Meanwhile the Giants have moved up 10 places from last year in the International Ice Hockey Federation's (IIHF) annual attendance study of European league ice hockey.
The Giants' average home gate was 4603 this season and they have now moved up to 70th in Europe, joining two other Elite League teams, the Nottingham Panthers (38th) and Sheffield Steelers (64th), in the top 100 of home gates for European clubs.
The Elite League (uk) has also moved up to the seventh best attended league in Europe, overtaking the Austrian EBEL.
The 300th anniversary of the birth of renowned landscape gardener Lancelot "Capability" Brown is being celebrated with a tree-planting ceremony.
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The Belfast Giants have awarded a testimonial game to long-serving forward Colin Shields.