The move, which was cleared in by the Cabinet Office under the National Security and Investment Act, is subject to conditions including the establishment of a national security committee "oversee sensitive work" and the formation of a technical group within that to monitor specific topics relating to cyber, physical and personnel security.
Under the conditions of the final order, the new committee will be required to provide regular updates and information to the government.
The Secretary of State, Oliver Dowden, said that these measures will mitigate any risks to national security.
The CMA said that neither party had offered any measures to address competition concerns.
In a joint statement, Vodafone and Three UK said: "We are pleased our proposed joint venture has been approved by the Government under the National Security and Investment Act.
"We are continuing to engage collaboratively with the Competition and Markets Authority to inform its ongoing review of our merger, which we strongly believe will strengthen competition in the UK’s mobile sector and enable a significant step-up in the UK’s mobile network infrastructure."
Vodafone and CK Hutchison announced plans in June 2023 to combine the UK businesses into a joint venture, with Vodafone owning 51 per cent and CK Hutchison 49 per cent of the new company.
This would bring their roughly 27 million customers under a new, single network provider.