The men can now delicately pluck the stalks out of cherries.
Sensors on the artificial hand are used to send signals directly to the nerves, the study, published in Science Translational Medicine, said.
Meanwhile, a Swedish team has made a separate breakthrough in artificial limbs - anchoring bionic arms directly on to the bone to improve control.
One of the beneficiaries of the American work was Igor Spetic, who lost his right hand in an accident four years ago.
He was fitted with a bionic replacement, but it was incapable of feeling the world around him.
He had to carefully watch what he was doing and judge by eye whether he was squeezing too hard.
A team at Case Western Reserve University attached sensors to the bionic hand and in surgery fitted "cuffs" around the remaining nerves, which were capable of delivering electronic stimulation.
The team could send different patterns of electronic stimulation to the nerves using a computer. These were interpreted in the brain as different sensations.
The team "mapped" these sensations to 19 different locations on the hand, from the palm to the tip of the thumb, and matched the sensors to the different electronic patterns of stimulation.
They then moved on to pressure and textures. Mr Spetic can tell, while blindfolded, whether he is handling different materials such as Velcro or sandpaper.
He has been using the sensing hand for two-and-a-half years. Another patient has been using the system for one and a half years.
Lead researcher Prof Dustin Tyler told the BBC: "They can do really fine delicate tasks now.
"We believe within five to 10 years we will have a system completely implanted so we would see a person in the morning, they would have the procedure to put electrodes on each nerve and a device for their pocket, so that when they turn it on they can feel their hands."
Mr Spetic said: "I would love to feel my wife's hand, just to hold hands would be the ultimate."
In both patients the modified hand had the added bonus of eliminating "phantom limb pain", in which patients still feel pain from the hand that is no longer there.
Meanwhile, scientists at Chalmers University of Technology in Sweden say they have implanted the first bone-anchored bionic arm.
The technique known as "osseointegration" involved connecting the arm directly to the bone, nerves and muscles in the residual stump of the patient's arm.
It gave the patient better control.
Dr Max Ortiz Catalan said: "We have used osseointegration to create a long-term stable fusion between man and machine, where we have integrated them at different levels.
"The artificial arm is directly attached to the skeleton, thus providing mechanical stability.
"Then the human's biological control system, that is nerves and muscles, is also interfaced to the machine's control system.
"Reliable communication between the prosthesis and the body has been the missing link for clinical implementation of neural control and sensory feedback, and this is now in place."