As well as shedding light on how life came to form on our own planet, the discovery has important consequences for our search for life elsewhere in the universe, the scientists say.
passengers stranded on tarmac amid plummeting temperatures
According to the "giant impact hypothesis", the moon was created from debris left behind when the Earth and a body the size of Mars smashed together.
The new theory proposes that the cosmic crash delivered most of the volatile elements essential for life to the Earth.
The "donor" planet was an embryonic world with a sulphur-rich core.
Laboratory experiments and computer simulations suggested that debris from the destroyed planet deposited the life elements on Earth.
They included most of the nitrogen and carbon found in living things, including humans alive today.
Lead scientist Rajdeep Dasgupta, from Rice University in Texas, said: "From the study of primitive meteorites, scientists have long known that Earth and other rocky planets in the inner solar system are volatile-depleted.
"But the timing and mechanism of volatile delivery has been hotly debated. Ours is the first scenario that can explain the timing and delivery in a way that is consistent with all the geochemical evidence."
Dr Dasgupta said the study could allow humanity to understand more about how the ingredients for life might form on other rocky planets like our own.
"This study suggests that a rocky, Earth-like planet gets more chances to acquire life-essential elements if it forms and grows from giant impacts with planets that have sampled different building blocks, perhaps from different parts of a protoplanetary disk."
More about: science