This comes after a ten-month investigation by UK competition authorities
The Competition and Markets Authority's (CMA) decision was largely expected following the release of its provisional findings last autumn.
The watchdog said on Friday that it had taken "extra time" to consider the views of customers and competitors, who had raised fears of rising bills and market dominance in telecoms provision.
But it concluded: "The merger is not expected to result in a substantial lessening of competition in any market or markets in the UK, including in relation to the supply of retail mobile, wholesale mobile, mobile backhaul, wholesale broadband and retail broadband services."
BT, which is seeking to become a major player in the mobile market again since spinning-off BT Cellnet in 2001, is the UK's largest fixed telecoms business.
EE, which also operates the Orange and T-Mobile networks, is the largest mobile provider with almost a third of its market.
A particular concern for the inquiry was whether a deal might affect the way the merged company provides wholesale services to rivals and whether it would remove incentives to continue to supply them.
But its chair, John Wotton, said: "In supplying services such as backhaul, wholesale mobile or wholesale broadband services a combined BT/EE would not have both the ability and the incentive to disadvantage competitors such that there would be significant harm to competition."
A deal will allow an enlarged BT to offer so-called 'quad play' to its estimated customer base of 35 million.
That is the prospect of TV, mobile, broadband and fixed phone line bills being rolled into one package.
Sky announced last year that it was entering a partnership with O2 to give its customers access to their own mobile network.
Sky was among companies which raised objections to the BT and EE tie-up arguing that BT's Openreach division, which provides many services for rivals in the telecoms sector, should be independent.
Mr Wotton said: "We have heard wider concerns about the sector, including about Openreach and its regulation by OFCOM.
"Our job has been to examine the specific impact of this merger on competition and consumers and, where relevant, we’ve looked at how these issues might be affected by the merger.
"There is also an ongoing OFCOM review into the sector and its future regulation, where such concerns may have more relevance."
TalkTalk responded to the CMA's decision: "We are disappointed, although not surprised, that the CMA has waived through the BT/EE merger, even though the new entity will be even more dominant than it was before privatisation 30 years ago.
"Given BT Group’s increased size and scale, the need to ensure that the UK’s broadband infrastructure is not neglected is more important than ever, and we have every confidence that OFCOM will take this into account when considering the future structure of Openreach."
It added: "There is a real risk that today’s announcement is the first step towards a slower, stagnant digital future."
The CMA's decision means the takeover is on track to complete by the end of March.
BT chief executive, Gavin Patterson, said: "The combined BT and EE will be a digital champion for the UK, providing high levels of investment and driving innovation in a highly competitive market.
"I have no doubt that consumers, businesses and communities will benefit as we combine the power of fibre broadband with the convenience of leading-edge mobile services. I look forward to welcoming EE into the BT family."