The documents describe Cohen's contract with the company, a relationship that earned President Donald Trump's personal lawyer $600,000.
The telecommunications giant declined to comment on the documents to the Post. The newspaper said, however, that AT&T did not challenge the authenticity of the documents.
Cohen's lawyer declined to comment to the Post.
AT&T had already confirmed it paid Cohen for "insights" on the Trump administration. In a Wednesday memo to employees, AT&T said that Cohen was one of the consultants it hired to better understand how the White House would approach a number of issues including antitrust enforcement.
The Justice Department sued to block the deal in November.
AT&T did not immediately respond to CNBC's request for further comment.