In the meantime it will undergo restoration.
The miniature measures 57cm x 25.5cm and is carved from a solid piece of red sandstone from the Bell Rock, which lies about 11 miles off Angus.
'Astonishing innovation'
It also features a polished bronze plaque inscribed: "MEMORANDUM This model of the Bell Rock Lighthouse presented by me to my daughter Mrs Warden was cut from the rock at the conclusion of the works in the year 1810 - Robert Stevenson."
Councillor Jim Millar told the BBC Scotland news website: "We're absolutely delighted that Angus Council has managed to secure this scale model of the lighthouse which has a direct link to the Stevenson family.
"The Stevenson family undertook one of the most difficult engineering projects of their period in building the Bell Rock lighthouse. It was an astonishing innovation that they managed to build it.
"And the fact the model is itself made from Bell Rock rock and presented to Stevenson gives it a very close link to Arbroath and we want to strengthen our connection with the Stevenson family."