"Salah al-Aruri was elected deputy to (Hamas leader) Ismail Haniya," an official in the movement told AFP on condition of anonymity, after a vote of its 18-member political bureau.
Aruri, who lives in exile after having spent almost two decades in Israeli jails, is alleged to have masterminded a series of attacks against Israelis in the occupied West Bank.
In 2015, the US Treasury issued sanctions against Aruri, along with other officials of Hamas, which is currently in negotiations with the internationally recognised Palestinian Authority about reconciliation.
There was no immediate reaction from Israel, which had previously accused Turkey of sheltering Aruri, to his appointment.
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Hamas, which runs the Gaza Strip and has fought three wars with Israel since 2008, is considered a terrorist organisation by the United States, European Union and others.
The Jewish state accuses Hamas of the 2014 kidnapping and murder of three Israeli teens in the West Bank that was part of an escalation towards war in Gaza that summer.
The Islamist group has never officially claimed responsibility for the killings but a video posted online shows Aruri allegedly praising Hamas's military wing for the "heroic" action.
Analysts say Sinwar is technically third in command following Aruri's appointment but has strong support in the military wing.
Aruri joined Hamas in 1987 and helped establish a military wing for the movement in the West Bank, according to Hamas media.
He was jailed by Israel for 15 years after being convicted of forming military cells in the territory.
Three months after his release in 2007 he was again jailed for a further three years, before being released and deported from the Palestinian territories.