The approval comes after the company addressed the EU commission's competition concerns.
The European Commission has given conditional approval to Dutch telecoms company KPN to sell its German subsidiary E-Plus to Telefónica for €8.6bn.
The approval comes after Telefonica Deutschland addressed the EU commission's competition concerns with a series of commitments including the sale of 20% of its mobile network to a mobile virtual network operator (MVNO) and the provision of an opportunity to acquire 10% of the network capacity.
Telefonica will have to provide 2.1 and 2.6 GHz frequencies to an interested party in order to enter the German market, and provide mobile sites and national roaming, as well as passive site sharing.
The company's existing contracts with wholesale partners will be extended until 2025 and the company will have to facilitate the transition to a guest network operator. According to the EU commission, these commitments offered by Telefonica will maintain healthy competition. However, it will reduce the number of independent mobile operators in Germany from four to three.
Telefónica Deutschland Holding CSO, Markus Haas, said: "We have now reached the most important milestone on our way to close the transaction."
"We welcome the decision by the European Commission. It underpins consolidation opportunities in Europe, fostering investments and mobile data business."
Telefónica Deutschland Holding CFO, Rachel Empey, said: "The new company will gain significant scale and efficiency benefits which will enable us to challenge the market with innovative products and services with great customer experience."
"Combining the strengths of both companies we will be able to offer a broader, deeper and faster mobile data experience, providing significant benefits for our customers."
Five national competition authorities including ones from Germany, Italy and the UK voted against the Commission's decision during a meeting last month saying that it may act against the interests of consumers, which was overlooked by the commission.
The commission said in a statement: "The acquisition of E-Plus by Telefónica would combine the number four mobile network operator in Germany, E-Plus, with the number three, Telefónica.
"The company resulting from the merger will have a market share roughly equivalent to the one held by each one of the other two MNO's, Deutsche Telekom and Vodafone.
"The merged company will also face competition from mobile virtual network operators - the so-called MVNOs - and service providers, which are hosted on the networks of the MNO's."