A Hamas delegation will then tour Arab capitals to seek financial support for their administration.
Hamas officials and Palestinian leader Mahmoud Abbas have agreed to convene parliament on 16 February, starting the process of forming a new government.
Hamas is under international pressure to renounce violence against Israel.
It has so far refused to do so, although it has said it is willing to merge its military wing into a Palestinian army.
A Hamas official announced the trip to Egypt on Saturday after talks with Mr Abbas.
It was the first time Mr Abbas had met with the Islamic militants since they beat his governing Fatah party in the Palestinian assembly election.
"We agreed with the president (Mr Abbas) to hold the first session of the Legislative Council on 16 February," Hamas leader Ismail Haniyeh told reporters in Gaza City after the talks with the Palestinian Authority President.
Mr Abbas has said he may formally ask a party to form a government only after MPs convene.
"Officially the first step is to inaugurate the parliament and then I will ask one side to prepare this government. I think this side will be Hamas," Mr Abbas said on Friday.
The Cairo meeting will follow up on the work of a Hamas delegation that travelled to Damascus earlier this week for talks with the movement's political leader Khaled Meshaal, a former physics teacher who lives in Syria.
Mr Meshaal has said the Islamist movement will never recognise Israel, despite threats from the US and EU to cut funding to the Palestinian Authority.
"We will never recognise the legitimacy of the Zionist state that was established on our land," he wrote in his column, To Whom It May Concern, in the al-Hayat al-Jadida newspaper.
"Our message to the United States and Europe is the attempts you are exerting to make us abandon our principles and struggle will be wasted and will not achieve any results."
However, Mr Meshaal said Hamas could offer Israel a ceasefire.
"If you are willing to accept the principle of a long-term truce then we will be ready to negotiate with you over the conditions of such a truce," he added.
The Israeli government has refused to deal with any administration containing Hamas unless the group recognises Israel and abandons violence and what it says is its "terror" infrastructure.