Haniya said: "Today is an occasion to celebrate. We have done everything."
Palestinians hope the deal will end fighting between secular Fatah and Hamas Islamists, as well as ease a crippling aid embargo of the Palestinian Authority by western governments.
The new government will be presented to parliament for final approval this weekend.
A Hamas official named the new interior minister as Hani Al-Qawasmi, an academic with no known political affiliation.
Israel has vowed to boycott the unity government, including non-Hamas ministers, unless it recognises the Jewish state, renounces violence and accepts interim peace deals as demanded by the Quartet of Middle East mediators.
Washington has also made clear to Palestinian officials that the embargo will not be lifted until the three conditions are met.
Saturday's special session is to begin at 11am (09L00 GMT).
Lawmakers will discuss the unity government's political platform and hold a vote of confidence, he said.