In a speech for Better Together, which opposes Scottish independence, he will say pensioner numbers in Scotland are rising faster than the UK average.
He will say Scots have paid UK National Insurance “all our lives” and it is “right” that the UK bears the costs.
The SNP said pensions were “more affordable” in Scotland than UK-wide.
Speaking at Glasgow University, Mr Brown will say the independence debate should not be about whether voters are “for Scotland or for the union”.
“In fact the real debate is between two Scottish visions of Scotland’s future,” the former prime minister will say.
“The nationalist one based on the breaking of all political links with the UK, and our vision based on a strong Scottish Parliament backed up by a system of pooling and sharing risks and resources across the UK.
“The whole point of sharing risks and resources across the UK is that it is right and proper that the British welfare state bears the rising cost of Scottish pensions as the number of old people will rise from one million to 1.3 million.”
For advice on Scottish Pension Call 0141 375 0313 or visit www.scottishpensionadvisers.co.uk