The former Labour leader makes the claim as he joins party colleagues Gregg McClymont and Lindsay Roy to launch the Keep Our British Pensions campaign.
Mr Brown, who is increasing his personal involvement in the referendum debate as part of the United With Labour campaign, will point out that polling evidence shows six out of 10 Scots believe pensions should be paid from UK and not Scottish taxes.
Speaking at the first pensions campaign event at Lochgelly Town Hall in Fife this morning, Mr Brown will say: "Our campaign shows that the sharing of pension risks across the United Kingdom is worth £200m extra each year to meet the greater needs of Scotland's pensioners.
"We have polling evidence that only 15% of pensioners favour independence and, indeed, 61% of all Scottish people believe that pensioners north of the Border should be paid from UK and not Scottish taxes."
Mr Brown, who represents Cowdenbeath and Kirkcaldy, will insist that Scotland must remain in the common UK National Insurance fund, which Scots have paid in to and accrued rights in all their working lives.
"These have to be honoured and continue to be honoured by the UK. It is bizarre that we would put Scottish pensions at risk at a time when pension spending in Scotland is rising faster than in the rest of the UK," explained the former PM.
"The number of over-60s in Scotland will grow from the current 22% of the population to 32% by the year 2035. The SNP cannot deny we face a higher bill in an independent Scotland when we lose the pooling and sharing that happens across the UK. It's why they set up a working party on the 'affordability' of pensions. Under a Labour government, Scots pensioner poverty fell from 33% in 1997 to 11% by 2010," added Mr Brown.
The first pensioners' referendum forum will also be addressed by Labour pensions spokesman Gregg McClymont, the MP for Cumbernauld, Kilsyth and Kirkintilloch East, and Lindsay Roy, the MP for Glenrothes.
Mr McClymont, who also has fears over occupational pension schemes, will say: "Because of EU rules, Scottish pension contributions for those schemes may have to rise or benefits may be lower; it could be both."
He will add: "There is absolutely no doubt we are better off spreading the risks as part of the Union."
The Scottish Government has already pledged to continue paying the basic state pension at the current rate if there is a Yes vote in September's referendum.