Additional Sessions Judge Sandeep Yadav also sentenced the third accused, Baljeet Singh Malik, to life imprisonment.
Kapoor and Shukla looked impassive while Malik seemed shocked upon hearing the sentence.
The parents of Jigisha Ghosh, who worked as an IT executive, welcomed the verdict, saying justice has been done to their deceased daughter.
"I had hoped for the two convicts to get death penalty and that is exactly what has happened," Jigisha's mother said.
The court imposed a fine of Rs 1.1 lakh against Kapoor, Rs 2.8 lakh against Shukla, and Rs 5.8 lakh against Malik and directed that Rs six lakh be given to Jigisha's parents as compensation from the amount collected from the convicts.
"Offence in the present case was committed in cold-blooded, inhuman and cruel manner," the court said.
"Innocent, helpless and vulnerable victim remained in the captivity of convicts for hours."
The court observed that to save herself Jigisha handed over her debit card and other belongings to the convicts. She also disclosed the PIN numbers of the debit card to the convicts.
The convicts killed Jigisha even after she pleaded for her life and were satisfied only by brutally mauling her to death, the court said.
"In other words, the convicts behaved in uncivilised and barbaric manner against a helpless girl," the court said.
"It is the level, magnitude and degree of brutality, attitude and mindset of wrongdoer behind the crime along with other factors which makes it a rarest of rare cases."
Gruesome crimes against women are on the rise and showing leniency will send a wrong message to the society, the court said.
Leniency will encourage criminals like the convicts while passing an appropriate sentence in such cases will go a long way in arresting the increasing trend of crime against women, the court said.
In awarding death penalty to Kapoor and Shukla, the court relied upon a report submitted by probation officer which recommended extreme penalty, observing that they cannot be reformed and would be a threat to society.
The probation officer said Malik's behaviour was normal throughout the trial.
The court on July 14 convicted the trio under Sections 302 (murder), 201 (destruction of evidence), 364 (kidnapping or abducting in order to murder), 394 (voluntarily causing hurt in committing robbery), 468 (forgery for purpose of cheating), 471 (using as genuine a forged document or electronic record), 482 (using a false property mark) with 34 (common intent) of the Indian Penal Code.
Public Prosecutor Rajiv Mohan sought maximum punishment for the convicts as they showed no remorse while killing Jigisha.
The convicts are also facing trial for killing journalist Soumya Vishwanathan and a taxi driver, the prosecution told the court.
Defence counsel pleaded for leniency, contending that the convicts were young.
Jigisha, 28, who was working with Hewitt Associates Pvt Ltd as an operations manager, was kidnapped and killed on March 18, 2009, after her office cab dropped her near home in south Delhi's Vasant Vihar around 4 a.m.
Her body was recovered on March 20, 2009, near Surajkund in Haryana.
Police later arrested Kapoor, Shukla and Malik for the crime.
