The banks, which had until 5pm on Monday to strike an agreement, said the combined group would “create the UK’s first true national competitor to the large incumbent banks” with over six million customers.
It would also see the group’s operations come under the Virgin Money brand in a licensing deal with Virgin Enterprises, the announcement said.
Under the terms of the all-share deal each Virgin Money share would be exchanged for 1.2125 new CYBG shares.
The companies said it represented a premium of 19% to the closing price for Virgin shares on 4 May at the start of the offer period.
The new share structure would see Virgin investors own approximately 38% of the combined group, they said.
But the announcement warned that the tie-up could result in as many as 1,500 job losses among the combined group’s current workforce of 9,500 as duplication and other cost synergies were identified.
It would have its headquarters in Glasgow with CYBG chairman Jim Pettigrew, chief executive David Duffy and finance chief Ian Smith all remaining in their roles.
Virgin Money’s chief executive, Jayne-Anne Gadhia, would not leave completely, the statement saying she had “agreed in principle” to serve in a consultancy role as a senior adviser to Mr Duffy.
She said of the deal: “The combination of Virgin Money with CYBG will have greater scale to challenge the big banks.
“It will also accelerate the delivery of our strategic objectives, particularly the expansion of the products we offer to
She added: “I am especially pleased that we have received a number of important commitments from CYBG.
“We have obtained assurances from CYBG regarding our employees (including a commitment to leverage the best talent from both CYBG and Virgin Money) and our Gosforth headquarters.
“The combined group will remain a committed voice behind the Women in Finance Charter as well as working to reduce the gender pay gap.
“This is a compelling deal for our shareholders, that accelerates value delivery and represents the beginning of the next chapter of the Virgin Money story.”