Would-be Iraqi female suicide bomber Sajida al-Rishawi and Iraqi Al-Qaeda member Ziad al-Karboli were hanged at 4:00 am (0200 GMT), government spokesman Mohammad al-Momani said.
A security source said the executions were carried out at Swaqa prison south of the capital in the presence of an Islamic legal official.
Jordan had promised to begin executing Islamic extremists on death row at daybreak in response to the murder of Maaz al-Kassasbeh, who was captured by IS when his plane went down in Syria in December.
Karboli was sentenced to death in 2007 on terrorism charges, including the killing of a Jordanian in Iraq.
Jordan had vowed yesterday to avenge the killing of Kassasbeh, hours after a harrowing video emerged online purporting to show the caged 26-year-old F-16 fighter pilot engulfed in flames.
The video - the most brutal yet in a series of gruesome recorded killings of hostages by IS - prompted global revulsion and vows of continued international efforts to combat the Sunni Muslim extremist group.
Jordan, a crucial ally of Washington in the Middle East, is one of several Arab countries that has joined a US-led coalition of countries carrying out air strikes against IS in Syria and Iraq.
Jordan's King Abdullah II, who was visiting Washington as the video came to light, described Kassasbeh as a hero and vowed to take the battle to IS.
The army and government promised to avenge the pilot's murder, with Momani saying: "Jordan's response will be earth-shattering."
Kassasbeh was captured in December when his jet crashed over northern Syria on a mission that was part of the coalition air campaign against the jihadists.
Jordanian state television suggested he was killed on January 3, before IS offered to spare his life and free Japanese journalist Kenji Goto in return for Rishawi's release.
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