The new company will also need to cap certain mobile tariffs and data plans for three years, as well as offer pre-set prices and contract terms for wholesale services for MVNOs.
These conditions will be overseen by the CMA and the communications regulator Ofcom.
"Having carefully considered the evidence, as well as the extensive feedback we have received, we believe the merger is likely to boost competition in the UK mobile sector and should be allowed to proceed – but only if Vodafone and Three agree to implement our proposed measures," Stuart McIntosh, chair of the independent inquiry group leading the investigation at the CMA said in a press release.