The US House of Representatives approved the bill in May, by a majority of 361 to 37, with 9 abstentions.
The objective of the bill is to dry the Hamas government of funds, thus leading to a breakdown of the government or a change in its stance.
"This legislation reflects our continued concern over the failure of the current government to renounce violence and terror, recognize Israel and respect its previous agreements and obligations," a White House official said.
In order for the Palestinian Authority to receive funding, the president must declare to Congress that the following conditions have been met:
Firstly, no ministry, agency, or instrumentality of the Palestinian Authority is effectively controlled by Hamas, unless Hamas has publicly acknowledged the Jewish state of Israel's right to exist and "committed itself and is adhering to all previous agreements and understandings with the United States Government, with the Government of Israel, and with the international community," including the Road Map.
Secondly, that the Hamas-controlled PA has made "demonstrable progress" toward purging individuals with ties to terrorism from its security services, dismantling all terrorist infrastructure with its jurisdiction, confiscating unauthorized weapons, arresting and bringing terrorists to justice, destroying unauthorized arms factories, thwarting and preempting terrorist attacks, and fully cooperating with Israel's security services.
Under this clause, they must also halt "anti-American and anti-Israel incitement in Palestinian Authority-controlled electronic and print media and in schools, mosques, and other institutions it controls, and (replace) educational materials, including textbooks, with materials that promote peace, tolerance, and coexistence with Israel."
Likewise, they must ensure democracy, the rule of law and an independent judiciary, as well as adopting democratic reforms such as financial transparency and accountability of government ministries and operations.
The United States, the European Union and others who regard Hamas as a terrorist group, have already cut off official direct aid to the government.
Despite this ban, the United States has been able to bypass the Hamas government and provide $468 million in humanitarian aid, primarily delivered by non-governmental organizations.
The new law Bush signed on Thursday does permit the continued flow of humanitarian aid for Palestinians and groups not linked to Hamas, like Palestinian President Mahmoud Abbas and his Fatah party.
AP and Reuters contributed to this report