Under the revised terms of the proposal, CYBG has offered 1.2125 new shares for each Virgin Money share, up from 1.1297 in the initial bid made last month.
Virgin Money shareholders would own approximately 38% of the combined group instead of 36%.
The deal values Virgin Money at £1.6bn.
Virgin Money shareholders would also be entitled to retain any dividend declared and paid in respect of the interim period ending 30 June 2018.
CYBG and Virgin Money said the move would create the UK’s first “true national banking competitor”, serving six million customers.
In a statement, CYBG said: “The proposed combination would provide a powerful full-service banking offer for around six million personal and business customers, bringing together the complementary strengths of CYBG and Virgin Money.
“With this further strengthened customer franchise and national reach, the boards of CYBG and Virgin Money believe the proposed combination would deliver increased value for shareholders and wider benefits to other stakeholders.”