The aim of the procedure, known as tissue engineering, is to create replacement body parts that work more like the real thing and are more durable than mechanical or animal valves that are currently routinely used in transplant surgery.
So far the technique has only been tested on animals, but scientists are hopeful that it will work on humans.
Dr Valentin Fuster, of Mt Sinai Medical Center, New York, said: "What's exciting is the possibility of making valves that are exactly like our own."
Experiments have been conducted on lambs with valves grown at Children's Hospital in Boston.
The valves are made from the patient's own cells and therefore have two major advantages:
Heart valves open and shut so blood will flow in only one direction through the heart.
Deterioration and leakage
When they deteriorate or leak, surgeons replace them with either mechanical valves - made from metal, ceramics, plastic and other materials - or valves taken from pigs and other animals.
However, animal valves tend to wear out, so they must be replaced.
Mechanical valves are more durable, but can cause blood clots, so recipients must taking blood-thinning drugs that can cause unwanted bleeding.
Additionally, young patients with heart defects must undergo several potentially life-threatening valve replacement operations as their hearts outgrow their mechanical valves.
The test-tube valves appear to answer the problem, but it likely will be several years before they will be ready for tests in humans.
Scientist start by removing cells from one of the lamb's arteries and growing a mass of the cells in a test tube.
The cells are when attached to a biodegradable valve-shaped scaffolding.
Within two weeks in a nutrient-rich culture, the cells multiply and completely envelop the scaffolding, which then decays.
Past attempts have failed
Past attempts to make working valves this way have failed because the valves, while they looked normal, were too weak to withstand the pressure of pumping blood.
This time, the researchers pumped fluid through the scaffolding as the valve grew, mimicking the effects of a pulse and conditioning the valve so it developed the strength of a normal one.
Six animals have had the new valves for about five months.
It is not long enough to evaluate how the valves will hold up over a lifetime, but they seem to be working without the need for blood thinners, although there has been some leakage of blood back through the opening covered by the valves.