Abbotsford House in Melrose, in the Borders, was reopened by the Queen in July after a £12 million, two-year refurbishment project.
Visitor numbers are double the forecast of the Abbotsford Trust for the period, and add to the 21,000 people who visited the attraction's gardens and visitor centre before the historic house reopened.
The trust hopes numbers will rise to 75,000 by the end of the year, almost matching the 80,000 who visited at the peak of the house's popularity in the 1970s.
Scott, who wrote Rob Roy and Ivanhoe, is heralded as the world's first best-selling novelist and creator of the historical novel.
His home opened to visitors in 1833, five months after he died.
Structural repairs have been made to crumbling stonework and 4500 objects from the house have been cleaned and catalogued.
Included in Scott's vast collection are Rob Roy's broadsword, dirk, sporran and gun; a blotter owned by Napoleon, which contains a lock of his hair; and a silver urn gifted to Scott by Lord Byron.
Two rooms previously not on public display have been added to the tour: Scott's original study which will host temporary exhibitions, and the religious corridor which features casts of stones from old ecclesiastical buildings.
Jason Dyer, chief executive of the trust, said: "We are delighted the newly transformed Abbotsford is rekindling an interest in this great man."
Funding for the revamp came from the Heritage Lottery Fund, Historic Scotland and Borders Council, as well as private individuals.