The board of Scottish Natural Heritage (SNH) sanctioned the slaughter in an effort to help preserve rare birds on the Uist isles.
Campaigners accused the organisation of "flying in the face of animal welfare advice and public opinion".
UIST HEDGEHOGS
"
I am convinced that today's decision was right for the birds
"
Dr John Markland
But the "tough decision" was defended by SNH chairman Dr John Markland.
The organisation's scientific advisory committee had ruled out the relocation of the creatures to the mainland on the grounds that almost half had died as a result of previous attempts.
However, it said it was willing to advise any animal welfare groups which wanted to fund a full scientific study of such a move.
More than 1,200 letters of objection were sent to SNH after it first raised the possibility of the cull.
A handful of hedgehogs were first introduced to the Uists in 1974 to help control slugs and snails in islanders' gardens.
Their numbers boomed but so did the threat to important populations of waders including dunlin, lapwing, redshank and snipe.
Preying on eggs
Recent surveys have shown that the numbers of some species of wading birds had dropped by nearly 60% in the last five years.
SNH said that the hedgehogs were jeopardising the populations of some birds by preying on their eggs.
Speaking after Tuesday's meeting, Dr Markland said: "This was a tough decision.
"On the face of it, culling seems cruel and moving animals to new homes on the mainland seems more humane.
"
We are planning to meet up with other interested organisations and individuals to list our options to get these perfectly healthy animals out before SNH can kill them
"
Ross Minet
Advocates for Animals
"The issues are far more intricate than that though."
He confirmed that SNH would offer advice on any proposed trials to relocate hedgehogs.
But he added: "It remains for those developing such ideas to ensure that the proposals do not involve any cruelty to hedgehogs, and are within the law.
"I am convinced that today's decision was right for the birds, right in terms of humane management of the Uist hedgehogs and right for the welfare of mainland hedgehogs."
The cull is due to begin next April as the animals emerge from hibernation.
Mass slaughter
Ross Minet of Advocates for Animals acknowledged that something had to be done, but argued that the hedgehogs should be humanely transferred to the mainland.
He said: "We are not entirely surprised that SNH have opted for the mass slaughter.
"We are planning to meet up with other interested organisations and individuals to list our options to get these perfectly healthy animals out before SNH can kill them.
"They are flying in the face of animal welfare advice and public opinion."