An examination confirmed the missile launcher is a military grade RPG 7 device with an accompanying warhead, police said.
Police say the discovery at a property on Hawthorn Street, off the Springfield Road in west Belfast on Tuesday, had saved lives.
A PSNI spokesman said it was a significant seizure that demonstrated the aim of a dissident terrorist campaign.
"It also displays the callous disregard these small groups have for the lives of those in local communities, given where it was stored and its potential (to) injure or kill anyone in the vicinity of where it would have been fired," they added.
A security alert was sparked after "a suspect explosive device" was found at a property in the area and up to ten homes were evacuated.
It was later confirmed that officers from the Serious Crime Branch found the military style weapons while conducting the search as part of an investigation into ongoing dissident terrorist activity.
Police will continue to use every lawful means to disrupt and dismantle groups committed to violence.
The seizure is still under investigation and further examination of the items is currently taking place.
"We would ask everyone in the community to work with us to remove these weapons from our streets," the spokesperson added.
"We would appeal for anyone with information about any such activity to contact us so that we can protect life and property and bring offenders before the courts."
Earlier this month Gardaí in Co Tipperary intercepted a suspected dissident republican haul of rocket launchers and explosives, which were believed to be en route to Northern Ireland.
Politicians have condemned those behind the storing of the weapons.
SDLP MLA for West Belfast Councillor Colin Keenan lives in the area where the weapons were found.
"Those who possess such cynical and dangerous weapons aimed to cause destruction are trapped in a negative mind-set. They do not reflect the views of the wider community who want to move forward," he said.
SDLP MLA for West Belfast Alex Attwood added: "The weapons that have been seized represented a very serious threat in themselves and confirm the continuing threat of dissident violence."
This find should give even greater encouragement to all of the community to assist the police whose good work has helped save lives.
SDLP MLA Alex Attwood
Ulster Unionist Policing Board Member Ross Hussey MLA welcomed the seizure by police.
Mr Hussey said: "The news of this seizure means that a lethal weapon has been removed from the streets and from the hands of terrorists who would have used it to cause death and destruction.
"Three weeks ago the Gardai in Co Tipperary seized a number of similar rocket launchers believed to be destined for the Real IRA in Northern Ireland and I commend the work of both the PSNI and the Gardai in combating the threat posed by violent criminal gangs.
"These seizures are tangible proof of the serious threat which these terrorist groups pose and I would appeal to all those who wish to see a peaceful future for Northern Ireland and its people to give no crumb of comfort or support to those who wish to divide and destroy this society."
West Belfast MP Paul Maskey said the find was a very worrying development that the community has been shocked by.
"I am glad that this is now off the streets and that no one will be hurt by this particular weapon," he said.
"I think we're very lucky that this weapon was never deployed on our streets because I have no doubt that many people could have lost their lives if this rocket had have been fired.
"People are saying this is not in their name, they do not want to see this in our community and are calling for dissident republicans to desist in what they are doing."
DUP MLA Jonathan Craig has praised the PSNI for seizing the weapons.
He said the seizure showed that there are still some people within our society who are determined to drag us backwards.
"The police serve our community and put themselves in danger doing so. Any successful action which removes dangerous weaponry from terrorists should be welcomed by all those committed to democracy and the rule of law.
"Community co-operation with the police is an essential component of an intelligence-led campaign against the dissident Republican criminals," Mr Craig, the party's Group Leader on the NI Policing Board, added.
Justice Minister David Ford congratulated the PSNI for recovering the military grade lethal artillery.
Minister Ford said: "It is clear that such a weapon had the potential to cause death and serious injury especially in a built up area.
"There is no place for any illegal weapons in our society and I would urge anyone with information to pass it to the police or anonymously to Crimestoppers."