The woman, failed suicide bomber Sajida al-Rishawi, and al-Qaeda operative Ziyad Karboli – both Iraqi nationals – were hanged at dawn, officials said.
The executions came hours after IS posted a video appearing to show pilot Moaz al-Kasasbeh being burned alive.
He was seized after crashing during an anti-IS mission over Syria in December.
Jordan had attempted to secure Lt Kasasbeh’s release in a swap involving Rishawi, but IS is believed to have killed him a month ago.
The militants had sought Rishawi’s release as part of a deal to free captive Japanese journalist Kenji Goto, but a video of his killing was posted online four days ago.
Rishawi had been on death row for her role in attacks in Jordan’s capital, Amman, which killed 60 people in 2005.
Karboli was convicted in 2008 of killing a Jordanian national.
The two prisoners were executed at 04:00 local time (02:00 GMT), government spokesman Mohammad al-Momani said on Wednesday morning.
Jordan earlier vowed an “earth-shattering” response after IS posted a video online showing what militants say is the pilot standing in a cage engulfed in flames.
One of the leading authorities in Sunni Islam condemned the killing, saying the burning to death of Lt Kasasbeh violated Islam’s prohibition on the mutilation of bodies.
In a statement released on Tuesday night, Sheikh Ahmed al-Tayeb, the Grand Imam of al-Azhar University in Egypt, called for the “killing, crucifixion of IS terrorists”.
Mamdouh al-Ameri, a spokesman for the Jordanian armed forces, said on Tuesday that Lt Kasasbeh had “fallen as a martyr”, adding: “Our punishment and revenge will be as huge as the loss of the Jordanians.”
Safi al-Kasasbeh, the pilot’s father, called for the Jordanian government to do “more than just executing prisoners”.
The blood of his son was the blood of the nation, he said, “and the blood of the nation must be avenged.”
“I call for [IS] to be eliminated completely,” he told reporters on Wednesday.
Jordan’s King Abdullah hailed Lt Kasasbeh as a hero, saying Jordan must “stand united” in the face of hardship.
The king decided to cut short a visit to the US after news of the pilot’s death, but he met President Barack Obama on Tuesday evening before flying home.
Many in Jordan have questioned its role in the air strikes against IS but the two leaders sought to reaffirm their joint resolve to destroy the group.
Mr Obama earlier said that if the video was real, it would be “one more indication of the viciousness and barbarity” of IS.
“I think it will redouble the vigilance and determination on the part of the global coalition to make sure they are degraded and ultimately defeated,” Mr Obama said.