The groups said that the Financial Conduct Authority and the Prudential Regulation Authority have given their blessing to the all-share deal.
CYBG had previously announced that the Yorkshire Bank brand will be phased out from the retail side of the bank over three years. The branches will all be renamed as Virgin Money.
No decision has been taken over whether the Yorkshire Bank brand will be retained for SME (small-and-medium-sized enterprise) banking customers.
A CYBG spokesman said: “CYBG encourages feedback from customers and the bank will be communicating with customers throughout the migration to the new brand.”
In a statement, CYBG said yesterday: “The offer (for Virgin Money) was made subject to the... receipt of the relevant approvals from the Financial Conduct Authority and the Prudential Regulation Authority.
“Virgin Money and CYBG are pleased to confirm that, on 3 October 2018, the FCA and the PRA gave written notice to CYBG, Virgin... of their approval of the acquisition.”
Investors in both firms voted overwhelmingly in favour of the deal last month. The union will see the owner of Clydesdale Bank, Yorkshire Bank and B brand takeover the Richard Branson-backed lender, creating an entity with around six million customers.
CYBG’s David Duffy will stay on as chief executive, leaving Virgin Money boss Jayne-Anne Gadhia to serve in a consultancy role as his senior adviser.
The boards of both CYBG and Virgin Money said they believed the deal will create the UK’s “first true national banking competitor”, offering a sound alternative to both SME and personal banking customers.
The combined group will rebrand as Virgin Money. Ms Gadhia has said that the tie up will “accelerate the delivery of our strategic objectives”.
The firms have previously said they recognise “that there will be a loss of jobs” as a result of the takeover, likely to number around 1,500. It is not clear at this stage whether the cuts will affect Virgin Money staff, CYBG staff or both.
Analyst Gary Greenwood at Shore Capital said: “The all-share combination of CYBG and Virgin Money has received regulatory approval from the FCA and PRA and is now expected to become effective on October 15. This is in line with management’s previously stated expectation for completion in the fourth quarter of 2018.
“We currently see fair value for CYBG at 345p (11 per cent upside) and for Virgin Money at 420p (14 per cent upside).
“While this is perhaps enough to begin to consider a more positive stance, we continue to see much better upside elsewhere in the domestic mainstream banking sector, with Lloyds being our preferred alternative.”
Yorkshire Bank was founded in 1859 in Halifax, West Yorkshire, by Colonel Edward Akroyd as a philanthropic organisation aimed at providing a means of saving for the working classes.
It was initially known as West Riding Penny Savings Bank. Deposits were strictly restricted to £30. Within a year the bank had more than 20 branches. It changed its name to Yorkshire Bank Limited in 1959. During the miners’ strike of 1984 to 1985, it offered deferments on the mortgages of striking miners during the dispute.
In 1990 National Australia Bank Group acquired the bank from the consortium of owning banks. In 2005, National Australia Bank merged Yorkshire Bank with Clydesdale Bank, creating the merged CYBG operation.
NAB announced that it planned to quit the UK market in 2014. The Clydesdale and Yorkshire Bank floated on the London Stock Exchange in 2016.