"The Court's decision could hardly have been more thorough, fact-based, and well-reasoned", David McAtee, AT&T's general counsel, said in a statement about Leon's ruling. "We are ready to defend the Court's decision at the DC Circuit Court of Appeals".
In his decision, Leon rejected the government's argument that acquiring Time Warner will give AT&T the power to raise prices that cable and satellite-TV companies pay for Time Warner content such as CNN, which in turn will lead to higher bills for consumers.
The document itself is over 200 pages and argues that the merger would significantly decrease competition.
In his almost 200-page opinion approving the merger, Judge Leon said that if the government asked him to stay the court order while the Justice Department appealed the case - in other words, to keep the merger on hold during the appeals process - he would refuse to do so.
First case of West Nile found in DeKalb County
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A spokesman for the Justice Department declined to comment on the filing. The Justice Department had 60 days to appeal the merger after it was approved. When the deal was announced nearly three weeks before the 2016 election, then Republican nominee Donald Trump rejected the transaction by stating, "It's too much concentration of power in the hands of too few".
Mr Trump has publicly feuded with Time Warner's CNN, calling it "failing" and a purveyor of "fake news".
AT&T argued, during the trial, that it needed to grow to survive in the era of Google, Amazon and Netflix.
Soon after the deal closed, AT&T announced a price increase for DirecTV Now, the company's online streaming video service.
Media commentators suggested Trump was critical of the deal because of his antipathy for CNN, which has lambasted his presidency and is a regular target for his Twitter attacks. The day after Leon delivered his ruling, Comcast made a $65 billion offer for 21st Century Fox, in an attempt to outbid Disney for Fox's entertainment assets.