The group updated its 1988 founding document, aimed at bridging internal divisions between Gaza and the West Bank and to end its global isolation as a terrorist group.
Haniyeh lives in Gaza, unlike Meshaal, who is based in Qatar.
Yahya Sinwar, a top commander in Hamas's armed wing, was named the movement's leader in the Gaza Strip in February. His position got enhanced in Hamas during Al-Aqsa Intifada because of his relationship with Sheikh Ahmed Yassin and because of the Israeli assassinations of the movement's leaders.
"Your freedom is a national duty and your dignity is our dignity", the new leader added, the Times of Israel reported. "The movement blesses this election which came in a consultative, democratic way that is homogenous with the lists and that shows the unity of the movement".
Hamas has ruled Gaza since 2007, after securing an overwhelming victory in legislative elections the previous year and ending 40 years of political domination by its rival Fatah party.
Some diplomats have however said Hamas would need to do much more to convince Western countries to end its isolation, noting that the changes announced so far could be merely window-dressing.
Haniya served as Palestinian prime minister after Hamas won a 2006 parliamentary election but was sacked by Palestinian President Mahmoud Abbas.
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Haniyeh, a former prime minister, competed for the post along with senior Hamas leaders Moussa Abu Marzouk and Mohammed Nazzal. "Yet, if circumstances can't help, he will not be able to make miracles".
"The terrorism label is one of the biggest challenges facing Hamas, which is seeking, via its charter, to tell the world that it's a nationalist group", he said.
"Therefore, it's not just a question of who leads, it's a question of the context and the circumstances in which a new leader leads". "The PA has chose to stop financing the Hamas "coup" in Gaza and we will reiterate the demand that Israel stop deducting funds from our revenues in favor of Hamas and its coup". "If a person is from outside Gaza, he won't talk about Gaza's ordeals and worries properly".
Last week, Hamas unveiled a new policy document easing its stance on Israel having long called for its destruction.
The intimation is that Hamas now accepts the State of Israel. The New York Times - as mentioned by Netanyahu - ran an article with a headline that read, "In Palestinian Power Struggle, Hamas Moderates Talk On Israel".
"We pay Israel for the electricity consumption in Gaza, while Hamas collects money from consumers and transfers those funds to its own budget", the official said.