According to the report, entitled 'War at Any Price', some $1.3 trillion of that figure will account for Iraq spending alone.
"The backbreaking costs of this war to American families, the federal budget and the entire economy are beyond measure in many ways," said Chuck Schumer, a Democrat senator.
"What this report makes crystal clear is that the cost to our country in lives lost and dollars spent is tragically unacceptable."
The report's ceiling figure of $3.5 trillion is $1.1 trillion higher than a non-partisan estimate by the congressional budget office last month.
The JEC estimate assumes a drawdown of US troops in Iraq but the retention of a large-scale US force in the country.
It also takes into account money spent and requested for the wars, interest payments on foreign loans used to finance the spending, and factors in higher costs of oil due to declined Iraqi production.
It also estimates the cost of repair and refitting military equipment and the outlay needed to retain soldiers in the ranks and economic disruption caused by the deployment of US army reserve units.
The report was released ahead of an expected house of representatives vote this week on a proposal to deliver $50bn to fund the wars for a four-month period instead of the $196bn budget request from Bush.
The proposal would require the withdrawal or redeployment of most troops in Iraq to begin immediately with a goal of ending combat operations within a year.
Bush has repeatedly resisted attempts by anti-war Democrats in congress to force him to accept troop withdrawal timelines for the Iraq force.
If Bush vetoes the bill, "then the president won't get his $50 billion", said Harry Reid, the senate majority leader.