Alaa Bader al-Hashemi, 30, was found guilty of stabbing to death school teacher Ibolya Ryan, 47, in a shopping mall toilet, Abu Dhabi newspaper The National reported.
She was also convicted of "creating a handmade bomb" she placed in front of an Egyptian-American doctor's home, it added.
The attacks took place within hours of each other in the UAE capital on December 1.
Tracked down using CCTV footage of her going into and out of the restroom where the teacher's murder took place and near the doctor's building, Hashemi was arrested 48 hours later.
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Hashemi was arrested at her home where her car was found with blood on the steering wheel and bomb making materials inside.
The National said that Hashemi "was also found guilty of sending money to Al-Qaeda in Yemen, knowing the funds would be used in terrorist acts".
The ruling was made by the Federal Supreme Court in Abu Dhabi, which means it cannot be appealed.
The president can, however, decide to overturn the sentence or reduce it.
Hashemi, surrounded by four police officers, "showed no emotion as the verdict and sentence were announced," the paper said.
International media have been denied access to her trial, which began on March 23.
Hashemi had asked the court to provide her with psychological help, saying she had "unreal visions" and would see "ghost-like people" due to a chronic mental illness.
The court ordered psychiatric tests which it said showed she was aware of her actions.
In March, Attorney General Salem Saeed Kubaish said that investigators found she had "listened to lectures by late Al-Qaeda leaders Osama bin Laden and Abu Musab al-Zarqawi, watched video clips of killings and beheadings," among other similar activities.