The finding comes as pressure grows in the UK for the drug to be legalised.
In the US experiments, a team from the National Institute on Drug Abuse trained four squirrel monkeys to give themselves shots of intravenous cocaine supplied through a catheter.
The animals did this by pressing a lever 10 times after a green light was illuminated in their isolation chamber.
Monkey lever
When saline was substituted for the cocaine, the monkeys stopped pressing the lever.
But when the salt solution was swapped for tetrahydrocannabinol (THC) - the active ingredient in cannabis - they quickly started activating the lever again.
In a typical one-hour session, they gave themselves 30 shots of THC - the equivalent in body size to an adult human smoking a marijuana cigarette.
The researchers also showed that the monkeys' compulsion for THC was reduced when they were given a second drug that blocks receptors on the cannabinoid receptors in the brain.
Lead researcher Dr Steven Goldberg told BBC News Online: "We compared the intensity of behaviour we that got with THC with the intensity of behaviour we got under exactly the same conditions with cocaine in another group of monkeys.
"We found the levels of behaviour were identical in the two groups of animals.
"So basically this is the first clear demonstration that the active ingredient in marijuana will maintain drug taking behaviour in experimental animals, and it indicates - from a pre-clinical standpoint - that it has the same potential for abuse that other drugs such as heroin and cocaine do."
Dr Goldberg admitted that his research could not take into account the social factors that would inevitably come into play when assessing the potential for abuse of cannabis among human users.
However, Dr Lester Grinspoon, a Harvard Medical School emeritus professor of psychiatry, dismissed the idea that the study proved that cannabis was addictive.
He said: " "This drug is not addicting. Clinical experience says that."
Medical use
Professor Tony Moffat, chief scientist with the UK's RPS, said large scale clinical trials were currently taking place to test the medical benefit of cannabis.
"Should that be the case then I believe that governments across the world will change their minds and make the use of cannabis for medicinal use legalised."
Professor Moffat said the trials were designed to ascertain the right dose for patients to take so that the beneficial effects outweighed the possible side effects.
UK Prime Minister Tony Blair has ruled out legalising cannabis for social use.