The council, which represents more than 1,400 private schools in the UK and abroad, reached its decision after a board meeting held yesterday.
The human rights barrister David Pannick KC will lead the challenge, to be brought on behalf of parents.
It comes after Rachel Reeves confirmed in the budget that a 20% VAT rate would be applied to private schools from January, with the government estimating it could raise £460m next year, potentially rising to £1.7bn by 2029/30.
Julie Robinson, the chief executive of the ISC, said: "This is a decision that has not been taken lightly and has been under consideration for many months.
"At all points throughout this debate, our focus has been on the children in our schools who would be negatively impacted by this policy.
"This focus remains and we will be defending the rights of families who have chosen independent education but who may no longer be able to do so as a direct result of an unprecedented education tax."
The government predicts private school fees could rise by an average of 10% due to the introduction of VAT.
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