The signing ceremony, held in capital Khartoum's "Friendship Hall" late on Sunday, was attended by international dignitaries.
Al-Bashir told the crowd: "This problem of Abyei, which was to undermine the unity in Sudan, will thank God, be used for building a unified Sudan."
Civil war fears
Last month, tens of thousands of local residents fled fighting between northern and southern troops in the remote central territory, raising fears that Africa's biggest country could be heading back into civil war.
|"This problem of Abyei, which was to undermine the unity in Sudan, will thank God, be used for building a unified Sudan"|
Omar al-Bashir, Sudan's president
Abyei has been a main point of contention for the Khartoum-based government in the north and the south's Sudan People's Liberation Movement (SPLM) since the former foes signed a 2005 peace deal that ended two decades of civil war fought along ethnic, religious and ideological lines.
Al Jazeera's Mohammed Vall said: "The two sides realised somehow that it is time to be serious about Abyei.
"[They] know that this issue can blow up the peace agreement between the two sides and take Sudan decades back to war and chaos."
At stake in Abyei is control over a large part of Sudan's oil wealth. The main town is surrounded by oilfields - believed to be worth half a billion dollars - connected by a key pipeline that runs through the disputed territory.
Kiir on Sunday said the new agreement will ensure that the resources in the area are used to improve life along the north-south border area.
He said: "With this road map we will be able to create a conducive security environment that will allow the return of the people of Abyei area to their homes with dignity and without fear."
Northern and southern troops, who are still in a standoff in the region, are to be replaced by a new "joint integrated unit" made up of soldiers from both sides.
Mustafa Mohammed Abdallah, professor of economics at Khartoum university told Al Jazeera that internationla arbitration may occur.
"If there is no reconciliation, then arbitration will lead to the International Court of Justice to set out the frontiers or the borders between the north and south," he said.
The two sides will also give the United Nations free access to the area to help displaced people return to their homes by June 30 at the latest.
"It was an important and historical meeting," Yasir Arman, the SPLM's deputy secretary general told reporters after discussions between the two leaders.
The final arbitration could take up to nine months to complete, Arman said, adding that the plan was endorsed by local tribal chiefs from the ethnic African tribe of the Ngok Dinka and the Arab tribe of Misseriah, who often fought over grazing rights.
Didiri Mohamed Ahmed, the northern official in charge of Abyei, said if the sides failed to agree on an international arbitrator after a month, they would turn to the Permanent Court of Arbitration based in The Hague to help them pick an organisation.
"It seems, from all the signs that we have right now, that they will definitely have to go to the Hague and seek the help of the international court there," Vall said.
The region will choose to join the north or south in 2011, when the entire south will vote on secession.