Criminals who can't explain how they got their money will be punished under a national scheme that allows the government to sweep up their assets.

A Senate committee unanimously recommended the "unexplained wealth" legislation be passed on Monday despite concerns being raised by the Law Council and Civil Liberties Australia.

The legislation will force people convicted of crimes to prove that their wealth was derived from legitimate sources, rather than the onus being on prosecutors to establish that it came from the proceeds of crime.

The new scheme will co-ordinate state-based frameworks that Home Affairs Minister Peter Dutton had argued were used by criminals to evade jurisdictions.

Banks will be forced to hand over any information they have on the unexplained wealth of a convicted client.