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.
She had been on death row for her role in attacks in the capital, Amman, that killed 60 people in 2005.
Karboli was convicted in 2008 for killing a Jordanian national.
'Punishment and revenge'
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 an online video showing what militants say is the pilot standing in a cage engulfed in flames.
Mamdouh al-Ameri, a spokesman for the Jordanian armed forces, said on Tuesday that Lt Kasasbeh had "fallen as a martyr".
"His blood will not be shed in vain. Our punishment and revenge will be as huge as the loss of the Jordanians."
Jordanian state TV reported that Lt Kasasbeh was killed a month ago.
Since then Jordan, which has joined the US-led coalition against IS, had tried to secure his release as part of a prisoner swap, offering to free Rishawi in exchange.
IS had sought her release as part of a deal to free captive Japanese journalist Kenji Goto. A video that appeared to show Goto's dead body appeared four days ago.
The BBC's security correspondent, Frank Gardner, says the latest video is aimed at a world already shocked by the calculated cruelty of Islamic State's actions.
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.
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.
Source: BBC