The US president had initially threatened to veto the bill over a provision providing $3.9bn in neighbourhood grants to help local governments buy and rehabilitate foreclosed homes.
Bush had said the money would benefit lenders who helped cause the mortgage meltdown, encouraging them to foreclose rather than work with borrowers.
However, he withdrew his complaint early last week, saying that homeowners
could not wait.
The US housing market has been hit badly by the subprime mortgage crisis, where people took out mortgages they later found they were unable to repay, slumping housing prices and tight credit conditions.
The law aims to assist debt-ridden homeowners by allowing them to obtain more affordable mortgages backed by the Federal Housing Administration (FHA).
The FHA could insure the mortgages, which would be available to homeowners who can prove they they can afford a new loan.
Banks would first have to agree to take a large loss on the existing loans in exchange for avoiding costly foreclosure.
Many Republicans, particularly those from areas hit hardest by housing woes, were keen to pass a housing rescue package ahead of crucial re-election contests in November's US elections.
A decision by Henry Paulson, the US treasury secretary, to request emergency powers to rescue Fannie Mae and Freddie Mac and create a regulator with stronger powers to oversee both government-sponsored companies, also helped the bill be approved by several key Republicans.
Both companies have seen their shares plunge by about 75 per cent since the start of the year as losses from their mortgage holdings threaten their financial survival.
Paulson had argued that a guarantee to prop up the companies by lending them money or buying their stock would calm investors and stabilise financial markets.
Budget analysts have estimatated that any potential bail-out of both companies by the current US administration could cost US taxpayers more than $25bn.
Meanwhile, a new housing report on Tuesday revealed that US house prices slumped in May at the steepest rate recorded so far.
The Standard & Poor's/Case-Shiller 20-city index fell by 15.8 per cent in May compared with a year ago, a record decline since its inception in 2000.