The deal sets out a political programme for a government including Hamas and Abba's Fatah faction which they hope will end their international isolation.
"We have finalised the elements of the political agenda of the national unity government... Hopefully, in the coming few days we will begin forming the government of national unity," Abbas said on Palestine TV.
Haniya will retain the post of prime minister and will therefore form the new government.
"This agreement was anticipated because the will was real and honest in the greater interest of the Palestinian people and to strengthen national unity and to protect [Palestinian] rights and principles," he said.
Abbas and Haniya now have to agree on the make-up of the cabinet.
It is hoped that international sanctions that have crippled the government since Hamas came to power in March, after defeating Fatah in general elections held in January, will be lifted once the new administration takes power.
Many countries have refused to deal with Hamas and have frozen financial assistance as they consider them to be a terrorist organisation.
A spokesman for Hamas, whose charter officially calls for Israel's destruction, has said that the group will not recognise the state of Israel.
"Hamas will continue to have its political agenda ... we will never recognise the legitimacy of the occupation," said Sami Abu Zuhri.
Israel welcomed the announcement but said that the administration must recognise Israel, renounce violence and ensure the release of Gilad Shalit, the Israeli army soldier seized by Palestinian fighters on June 25.
Mark Regev, the Israeli foreign ministry spokesman, said that if the Palestinian government met these conditions "this would open the door to accelerated talks and create new momentum in the peace process".
The administration has come in for criticism in recent weeks, including strikes by doctors, teachers and other employees throughout the Palestinian territories who are angered by the non-payment of salaries for the past six months.
Hamas has been unable to pay most of the government's 170,000 employees any wages since it came to power because of sanctions imposed by the US and EU, both of which consider Hamas to be a terrorist group.
Abbas has called for an end to the strikes.
"We call for a return to work and the end of the strike because all the sons of the Palestinian people should unite together in the national interest," he said.