The new truce - signed on Wednesday - gives the rebels an additional month to assemble at two camps in southern Sudan.
Once they have reached these "safe zones", LRA leaders and Ugandan officials will meet in Juba, the capital of south Sudan, to negotiate an end to the war.
At the peace talks which began in July, Riek Machar - south Sudan's vice president and chief mediator, said: "We hope today's agreement creates a much better atmosphere."
Under the previous deal, Lord's Resistance Army (LRA) fighters were to gather at the two assembly points - but they failed to show up.
Monitors said that both sides had broken the initial agreement, the rebels by not going to the meeting points and Ugandan forces by getting too close to the eastern assembly point at Owiny-Ki-Bul.
The new agreeement not only gives the LRA more time to reach the camps, but also takes new steps to guarantee the fighters' safety.
"The forces of the parties shall remain as far apart as 15km of the specified perimeters," the new truce agreement says.
Other groups, including journalists and diplomats, have also been banned from visiting the assembly areas without Machar's permission.
Ugandan negotiators and LRA representatives in Juba welcomed the new deal.
Kony has called for rule according
to the ten commandments
Ruhakana Rugunda, the head of the Ugandan team and internal affairs minister, hugged each of the LRA delegates after the signing.
"This will help build confidence and further consolidates the peace process," he said.
Martin Ojul, the head of the LRA negotiators, agreed: "We are very happy with this agreement because it has removed some of the impediments that were disturbing us."
The LRA has led a uprising against president Yoweri Museveni's government since the mid-1980s, leaving thousands dead and forcing 1.7 million people to flee from their homes, according to relief organisations.
The United Nations has accused the LRA of cutting off the tongues and lips of innocent civilians and kidnapping thousands of children and forcing them to be soldiers or sex slaves.
The international criminal court has issued arrest warrants for five LRA commanders.
In the past, Joseph Kony, the leader of the LRA has called for Uganda to be governed according to the Bible's ten commandments.
More recently, their negotiators have recently said their group's intention is to draw attention to the government's neglect of northern and eastern Uganda.