They believe their discovery will help research into a vaccine or cure for the deadly virus.
Ebola first emerged in 1976 in the Sudan and Zaire; the virus, which causes haemorrhagic fever, kills anywhere from 50-90% of its human victims.
Ebola is currently handled in highly secure labs, and the researchers say by removing a single gene from the virus they have stopped it replicating.
They say this process genetically disarms the virus, making it safe for scientists to handle.
The researchers from the University of Wisconsin at Madison, say the need for the most stringent bio security levels for any laboratory working with Ebola means that very few research institutions have the capability to do this.
Bio security levels 4" (BSL4) are needed which requires researchers to wear bio safety suits with their own air supply and the air pressure in the room must be less than the pressure outside, so any leak would mean air flowing inwards rather than outwards.
Such measures say the team guarantees that anything more than small-scale studies of the virus are very difficult to arrange and research is limited to possibly as few as a dozen laboratories worldwide.
The researchers say if Ebola could be kept in a viable form but with the risk of infection removed, then conventional research laboratories might be able to study it.
The researchers believe the key is to remove one of Ebola's eight genes, called VP30, as without it, the virus cannot replicate within host cells by itself.
However, in order that virus could still replicate so it could be studied, they developed monkey kidney cells which contained the protein needed.
The researchers say because the cell was providing the protein, and not the virus itself, it could only replicate within those cells, and even if transferred into a human, would be harmless.
To prove this happened they used the monkey cells for dozens of "cycles" of infection and replication, without once encountering a form of the virus capable of making another creature sick.
Lead researcher Yoshihiro Kawaoka, an internationally acclaimed virologist, says as the altered virus does not grow in any normal cells, the system can be used for drug screening and for vaccine production.
However, some Ebola experts and researchers are sceptical and say more proof is needed to convince them that the modified virus could do no harm and not cause disease in live monkeys.
The symptoms for Ebola include high fever, severe headache, muscle, joint, or abdominal pain, severe weakness and exhaustion, sore throat, and nausea.
As the infection progresses symptoms that are more serious include diarrhoea, vomiting blood, organ damage, and internal bleeding occur.
A new strain of Ebola, which has emerged only in remote areas of the world, was recently identified in Uganda where it has killed at least 40 people.
Kawaoka says this is an emerging virus and it is highly lethal, but because of the BSL 4 requirement, knowledge of the virus is limited.
The research is published in the Proceedings of the National Academy of Sciences journal.
