The bank said it would offer 423.2 million shares, representing 28.2 percent of Britain's largest car insurer, and retain only 4.2 million shares to satisfy long-term incentive plan awards granted to Direct Line executives.
RBS was ordered by European regulators to sell all of Direct Line by the end of 2014 as a penalty for its bailout in 2008 that left it 81 percent-owned by the British government.
RBS, which spun off Direct Line in the wake of the financial crisis, said on Wednesday the pricing of the shares it plans to sell would be determined by a bookbuilding process that would start immediately.
Direct Line's shares closed up 0.8 percent at 263.34 pence on Wednesday, valuing the 423.2 million shares the bank plans to sell at about 1.1 billion pounds ($1.8 billion).
Goldman Sachs International, Morgan Stanley Securities Ltd and UBS Ltd will act as joint bookrunners in the offering, RBS said on Wednesday.
RBS, which is due to report results on Thursday, plans to shrink its investment banking and international operations as part of a revamp in which the group could shed up to a quarter of its 120,000 workforce, sources familiar with the matter said last week.
Shares in RBS closed down 2.3 percent at 358.4 pence on the London Stock Exchange, making the stock one of the top percentage losers on the FTSE-100 Index .FTSE.
Earlier on Wednesday, Direct Line reported a 70 percent rise in full-year pretax profit, helped by fewer home insurance claims. Net earned premiums fell 5 percent to 3.52 billion pounds.
The company, which also offers home, travel and pet cover, said it would focus on profitability this year, in a market where competition has intensified due to discounting, price-comparison websites and market reforms introduced last April.
"We will price according to the value that we want to get and according to the claims trends we see," Direct Line Chief Executive Paul Geddes told Reuters in an interview.
The Automobile Association (AA), which has tracked car and home insurance in Britain since 1994, said the downward trend in motor premiums could be about to end.
The association said it expected premiums to rebound by up to 12 percent this year as car insurers come under increasing pressure from their directors to stop writing higher volumes at unprofitable rates.
"They won't be able to cut prices any more. They'll have to start putting prices up," Simon Douglas, director of the AA, told Reuters on Tuesday.
Geddes declined to comment on whether Direct Line would raise its premiums in 2014.
"The market is set by some players that are prepared to set low prices," he said. "Profit will stay down while there are enough people prepared to write at those prices."
Geddes said that Direct Line cut its motor premiums by 3-4 percent over the last year, versus a drop of 6-8 percent in the wider market.
In a bid to reduce the number of personal injury claims made annually in Britain, the government in April banned the payment of referral fees to solicitors, insurers and claims management firms, driving premiums down.
Despite this, claims rose last year, the AA's Douglas said, adding that many insurers would not have enough income to compensate for this increase.
British motor insurers are expected to report a combined ratio, a measure of profitability, of about 114 percent in 2014, compared with 109.4 percent last year, according to a report by Ernst & Young.
A ratio above 100 percent means an insurer pays out more in claims than it earns in premiums.
The insurer said it aimed to achieve a combined ratio of between 95 percent and 97 percent in 2014.
It said it would pay a total dividend of 20.6 pence per share and that it was on track to meet its 1 billion pound cost target for 2014.
"2013 earnings and adverse weather losses so far in 2014 are better than our expectations," RBC Europe analyst Gordon Aitken said, maintaining his "outperform" rating on the stock.
The intrinsic value of Direct Line's stock is 497.4 pence, according to Thomson Reuters StarMine's model of how much a stock should be worth when considering expected growth rates over the next 15 years.
($1 = 0.5994 British pounds)
Additional reporting by Esha Vaish, Editing by Supriya Kurane, Robin Paxton and Saumyadeb Chakrabarty