The deal is worth $US110 billion ($A156 billion).
Justice officials determined the transaction did not pose a threat to competition, according to the sources.
Politico on Friday reported, citing one source, the department approved the merger without requiring any divestitures, behavioural remedies or concessions.
Spokespeople for Paramount and the DOJ spokesperson declined to comment.
The clearance gives Paramount another regulatory green light to point to as it seeks to ward off a potential challenge to the deal by California and other states.
In April, Paramount also asked the Federal Communications Commission (FCC) to approve foreign investments backing the acquisition. US senators have raised concerns about Middle Eastern sovereign wealth funds and Chinese companies taking part.
The FCC has yet to make a determination. Analysts had expected the DOJ not to challenge the deal because of Paramount's political connections. Paramount CEO David Ellison's father, billionaire Oracle co-founder Larry Ellison, has cultivated ties with President Donald Trump, and the company has hired former Trump officials.
Assistant Attorney General Omeed Assefi had said politics would "absolutely not" drive the DOJ's review of the transaction.
Paramount has argued the deal has no antitrust problems, and said the combined company would increase competitive pressure on Disney and Netflix.
However, several in Hollywood - including actors, directors, writers and producers - have expressed concern the merger would result in fewer jobs, and less diversity of storytelling.
California, New York and other US states are preparing a lawsuit to block the deal, sources familiar with the matter told Reuters last week.
