Manannán Mac Lír
The six-foot Manannán Mac Lir sculpture disappeared from Binevenagh Mountain, near Limavady, last month.
It was created by John Sutton, who worked on the Game of Thrones TV show.
At a meeting on Tuesday night, Limavady Borough Council voted to replace the stolen artwork with a sculpture "as similar to the original as possible".
Its chief executive, Liam Flanigan, told elected members that he had received letters from across the world in the wake of the sculpture's theft.
"We've had offers of support from the States, Canada and New Zealand. The response has been worldwide, with many people offering to contribute to the replacement of the sculpture."
The council is set to approach the original artist to request financial quotes for the replacement and will seek estimated costs for reinforcing the new artwork, to ensure it is more difficult to remove from its mountainside perch in future.
Councillors also agreed to set up a fund to allow members of the public to make donations towards the cost of the reinstatement.
Manannán Mac Lir is a sea god from Irish & Manx mythology and the statue had become a popular tourist attraction in the area.
Its disappearance remains a mystery, but police have said they are investigating a "religious aspect" to the theft.
Those who cut down the statue left a small wooden cross in its place, bearing the words 'You shall have no other gods before me'.
Mr Sutton has said he believes it would have taken a number of men with angle grinders several hours to remove the heavy, man-size figure from its base.
At Tuesday night's council meeting, Sinn Féin's Rory Donaghy proposed that the replacement be based as closely as possible on the original £10,000 sculpture.