The business where former Royal Bank of Scotland chief executive Stephen Hester is now leading a turnaround said the deal was expected to result in a gain of about £110m and would add about £95m to the company's tangible net assets.
RSA underwrites a mix of commercial and retail business in Singapore and Hong Kong. Allied World Assurance provides property, casualty and speciality insurance and reinsurance services.
RSA earlier this month posted an interim pre-tax profit of £69m, following a £494m loss in the second half of last year.
The London-headquartered insurer was hit by three profit warnings in the second half of 2013, and an accounting scandal in Ireland for which it is facing a big fine. That led to the departure of chief executive Stephen Lee , who was replaced in February by the former RBS chief.
Mr Hester has said the recovery is "ahead of our expectations" and thanked shareholders for their patience on the absence of a dividend in the first year of a three-year strategic plan.
Ratings agency Fitch said after the results that it believes "some uncertainty still remains about the size of further write-offs, reserve strengthening and the cost-reduction programme, despite the significant increase in the company's capital resources resulting from management actions".
RSA shares were up 0.2p to 437.70 yesterday.