The star, who has close connections to the Cove area in Argyll and Bute and specific ancestral ties to the Linn Botanic Garden run by Mr Taggart, pledged an undisclosed sum to the search fund.
The 53-year-old Four Weddings And A Funeral star met Mr Taggart on a visit to the garden with his father James - who spent part of his childhood living on the estate - seven years ago.
Grant's backing comes as supporters await an update on the search for the 42-year-old who went missing in the north of the country while on a plant-documenting expedition.
His message read: "From Hugh Grant and his father James with very good wishes."
The close-knit Cove community have raised thousands of pounds to keep the search going and the actor's involvement came as a result of the link between the Taggart and Grant families.
The spectacular Linn Villa in the grounds of the botanic garden was once the home of Mr Grant's great-grandfather William Martin, provost of Cove and Kilcreggan, who commissioned the first garden on the estate.
The star's grandmother Jesse Martin also grew up at the house and his dad, James Grant, spent his teenage years there in the 1940s while his own father, Major James Murray Grant, was fighting during the Second World War.
Dr Jim Taggart, Jamie's father, bought the villa in 1971 and turned the garden into an international attraction.
Mr Grant and his father James made their trip to the garden in 2007 when Mr Taggart snr gave them a tour and discussed their family histories.
Mr Taggart said he believes one of the fundraisers contacted Mr Grant to tell him about the search and he added he had been encouraged by the level of support it had received.
He said: "A lot of people have been massively generous - thanks to everyone."
Search parties have focused on Hoang Lien National Park area and the most recent have been concentrated in the Ban Khoang Mountain area.
A series of sightings in four locations have been confirmed in recent weeks by searchers but all date to the time he went missing.
Mr Taggart was last seen on the main Sa Pa Town road heading west and at one stage was trying to obtain a permit to the national park.
Park authorities are working in tandem with local trackers hired by friends and family of Mr Taggart, who have also set up a Facebook campaign.
The searches cost about £1200 per tracker per week including all equipment, with a reward for the discovery of Mr Taggart.