The result for the year to March 31 is more than double the £152 million in 2012 - when there was one less trading week - as the state-owned firm benefits from the boom in online shopping and recent efforts to modernise the business.
Chief executive Moya Greene, who last year returned the core postal business to profitability after four successive years of losses, said it was a strong performance and that the transformation of Royal Mail was under way.
The core postal business, which delivers the six-days-a-week universal service to 29 million addresses, reported operating profits of £331 million and improved its margin from 0.5% to 3.9%. Parcel deliveries now account for almost half of the group's revenues of £9.3 billion in the last year.
The performance is expected to encourage the Government to cash in on the turnaround by pressing ahead with a privatisation this year, despite opposition from unions representing postal workers and managers.
However, unions have warned that services will go into decline if the business is sold off.
The preferred option is believed to involve the public buying shares alongside City investors, in an echo of the "Tell Sid" campaign that pioneered the public sale of shares in British Gas in the 1980s.
At least 10% of the shares have been earmarked for the workforce, although it is not known whether staff will get them for free.
The Communication Workers Union (CWU) will this week start balloting Royal Mail workers on whether to boycott the post of rival companies in a move which could lead to millions of items being left undelivered. Around 120,000 members of the CWU will vote from Wednesday, with the result due on June 19.