The group said the talks would begin on Sunday and would assess how far the government was "ready to accept the demands of the people".
The negotiations would be the first ever to be held between the government and the officially banned Brotherhood.
President Hosni Mubarak has rejected protesters' demands that he quit now.
Mr Mubarak - who has been in office since 1981 and has tolerated little dissent - has said he will not stand in elections due in September but will not resign immediately as this would cause chaos.
Huge crowds have been on the streets of Cairo and other cities in the past two weeks demanding his immediate resignation and calling for democratic reforms.
The Muslim Brotherhood had previously said it would not take part in negotiations between the government and opposition groups.
But a spokesman told Reuters: "We have decided to engage in a round of dialogue to ascertain the seriousness of officials towards the demands of the people and their willingness to respond to them."
A spokesman told the AFP news agency the dialogue was also aimed at ending "foreign or regional interference" in the situation.
The Islamist group is Egypt's most influential and well-organised opposition but it remains officially banned and its members and leaders have been subject to frequent repression.
Mr Mubarak has blamed it for the unrest and said that if he leaves, the group will exploit the ensuing political chaos.
The Muslim Brotherhood denies accusations that it is seeking to create an Islamist state in Egypt.
The BBC's Jon Leyne, in Cairo, says the Brotherhood is undoubtedly a force in Egypt but it is itself divided and unclear in its intentions. After an election it may be part of a coalition.
He says that although the Brotherhood has indicated it will only talk about Mr Mubarak's departure, the talks are still a gamble as there is deep scepticism in the ranks of the protesters.
Our correspondent says the government would like to see the protesters isolated by those who simply want to get back to work, but with what the demonstrators have been subjected to, there is no sign of them giving up.
The opposition demonstrators continue to occupy Cairo's Tahrir Square, with the protests entering their 13th day, although the numbers have fallen from Friday's huge rally.
One protester told the BBC by telephone that people in the capital were returning to work and there was transport around, but the square was still occupied by the protesters and the government was not happy with that.
The military has been attempting to re-open the square to the public in an attempt to restore normality, and to confine the protests to a small area.
"You all have the right to express yourselves but please save what is left of Egypt. Look around you," said army commander Hassan al-Roweny, addressing the crowds on Friday evening through a loud speaker.
But hundreds of people then attempted to prevent the army from entering the square - some lay on the ground in front of the tanks to block their progress.
The BBC's Jim Muir in Cairo says they fear the protests would become irrelevant if they were confined to a smaller area - but he adds that relations between the soldiers and the demonstrators have remained friendly.
The US - a key ally of the Mubarak government - has called for a swift transition of power, although it has not explicitly told Mr Mubarak to leave.
It has also encouraged all parties to fully engage in talks with opposition groups.
US Vice-President Joe Biden phoned his Egyptian counterpart Omar Suleiman on Saturday, and called for "credible, inclusive negotiations for Egypt's transition to a democratic government to address the aspirations of the Egyptian people", the state department said.
The entire leadership of the ruling National Democratic Party (NDP) resigned en masse on Friday, apparently in response to the protests.
Two of Mr Mubarak's allies, including his son Gamal, lost their posts while Hossam Badrawi was appointed secretary general.