The deal, which will cost BT £12.5 billion will see it become a major contender in the mobile market again.
Competitors, including Vodafone, thought the acquisition would make BT too powerful.
The CMA, however, believes that there will be no real harm done to either ordinary people on the street or to the mobile industry.
Although the CMA has given provisional approval to the merger, competitors will have a further three months to make further objections before a final ruling comes in January next year.
If the deal does go through, the four biggest operators in the UK will be Vodafone, O2, Three and BT-EE.