Trucks carrying supplies to US troops allegedly pay the firms to ensure their safe passage in dangerous areas of Afghanistan.
The convoys are attacked if payments are not made, according to allegations in a US military document.
The congressional report follows a six-month investigation.
The document states that trucks carrying food, water, fuel, and ammunition may be supplying up to $4 million (£2.7m) per week to the firms.
A US congressional committee is expected to hear the evidence on the investigation from senior officials at the US Department of Defense later on Tuesday.