Taking on Microsoft's Kinect system, Leap says that its technology represents "an entirely new way to interact with your computers" that is "more accurate than a mouse, as reliable as a keyboard and more sensitive than a touchscreen".
Leap Motion's technology allows you to control a computer in three dimensions with just your natural hand and finger movements.
The company, which was founded in 2010 by Michael Buckwald and David Holz, and has raised $14.55 million to date, has patented software that creates a three dimensional interaction space of four cubic feet in which users can control the computer.
According to Leap, the system is accurate to within 1/100 of a millimetre, and allows various precise touch-free gestures, such as pinch-to-zoom.
The technology creates a 3D workspace in front of the screen, and is said to be the first product to accurately sense the individual movements of all 10 of the user's fingers.
In a veiled slight on Microsoft's Kinect for Windows, Leap said that existing motion sensing technology is "crude, inefficient and often frustrating", while touchscreen technology is "limited by a two-dimensional workspace and scale restraints".
Leap Motion chief executive Buckwald said that the technology is flexible and so could expand beyond computers to smartphones, tablets and even refrigerators.
"It was this gap between what's easy in the real world but very complicated to do digitally, like moulding a piece of clay or creating a 3D model, that inspired us to create the Leap and fundamentally change how people work with their computers," he said.
"In addition to the Leap for computers, our core software is versatile enough to be embedded in a wide range of devices, including smartphones, tablets, cars and refrigerators.
"One day 3D motion control will be in just about every device we interact with, and thanks to the Leap, that day is coming sooner than anyone expected."
A video introducing the Leap system shows a user performing various touch-free tasks, ranging from basic navigation of web pages to precise virtual drawing in 2D and 3D.
The system is also usable for gaming, as the video shows someone playing a first-person shooter and Rovio's hit digital title Angry Birds.
Leap works by plugging directly into a USB port, before calibrating to the machine's settings. The user can then start controlling their computer with touch-free hand and finger movements.
Sensitivity settings can be fine-tuned, while custom gestures can also be created and multiple Leap PCs can be networked together.
"Breakthroughs in technology come in all sizes, but often the very biggest disruptors come in very small packages - the computer chip, the mouse, the smartphone and now the Leap," said Bill Warner, the founder of Avid Technology and a Leap Motion investor.
"Roughly the size of your pinky finger, I believe the Leap is the future of how people will interact with their devices. What's previously been an expensive special effect in movies is now an affordable everyday reality, in full 3D.
"With the Leap, you use both hands and all 10 fingers to work within your computer's virtual environment just as easily as you do in the real world."
The Leap is said to be 200 times more sensitive than existing technologies, yet it costs just $69.99 (£44), under a third of the $249 (£157) Microsoft charges for Kinect for Windows.
Pre-orders for the product started last week, and the Leap is set to ship in the winter.
Leap Motion is also accepting requests for free developer kits in the hope of fostering a "wide array of Leap-based applications", potentially covering fields such as medical imaging, robotics, art, training simulators and virtual-reality environments.