The government is selling a 5.2 per cent of the high street lender, equivalent to 600m shares, to take its interests down to 73.2 per cent.
Following the sale, the state will still be left with a stake in RBS worth around £32bn.
Chancellor George Osborne gave the go-ahead for the sell-off just days after the bank revealed an encouraging set of profits, pointing to a steady turnaround in the health of the wounded group.
It marks the first step in the rehabilitation of the company after it was rescued in 2008 by a £45bn government bailout.
Shares at the time were worth 502p, but have since tumbled to 337.60p, crystallising a loss for the government.
Osborne signalled the plans for RBS in his Mansion House speech by saying the taxpayer “may get a lower price than Labour paid for it”. Bankers from Goldman Sachs, Morgan Stanley, Citigroup and UBS hit the phones after markets closed last night to flog the shares at a 2.3 per cent discount to City fund managers.
RBS shares slid 1.34 per cent during trading yesterday as investors held off from buying shares in anticipation of the sale.