Scarborough Borough Council' s planning committee yesterday voted six for and six against the plans, before committee chairman councillor Subash Sharma made a casting vote of approval.
The sculpture, created by artist Ryan Gander OBE, echoes the structure of a concrete coastal-erosion barrier.
The approval comes after a similar 6ft 5in sculpture to be sited near Whitby Abbey was withdrawn after over 80 complaints that it would be an "eyesore".
No objections were made against the latest Scarborough plans, although councillors did question why this location was chosen for the sculpture and why people would have to pay to enter the English Heritage castle grounds to see it.
Speaking at yesterday's meeting, councillor John Casey said: "I think it is totally the wrong location for something like this.
"If it wants to raise awareness of coastal defences and erosion, it would be much better placed on Marine Drive where it could be viewed 365 days a year for free."
Councillor Rich Maw added: "To me it just doesn't look like anything I would pay to go visit. I have seen megalithic stone walls that are thousands of years old and look prettier than that."
Meanwhile, councillor Phil Kershaw spoke in favour of the plans, saying any kind of public art should be "applauded".
Planning permission was granted for the sculpture to be sited at the castle grounds for up to 10 years. This comes after a decision was deferred earlier this year.
The project has been backed by £140,000 from the government’s Town Deal Fast Track Fund and is part of the Wild Eye trail, a collaboration between Scarborough Council, English Heritage and Scarborough-based environmental art charity Invisible Dust.