Najib Razak said relatives of the flight's 239 passengers and crew had been told of the "heartbreaking" news.
Inmarsat used new techniques to detect the plane's course, he said.
The UK's Air Accidents Investigation Branch, which probes serious civil aircraft incidents, was also involved.
Malaysia Airlines flight MH370 went missing after taking off from Kuala Lumpur on 8 March.
Mr Razak's announcement came as the international search effort reached a fifth day of operations in the southern Indian Ocean.
'Quite astounding'
Inmarsat has told the BBC it gave the Air Accidents Investigation Branch (AAIB) the new data on Sunday - stressing it needed to be checked before it was made public.
The firm said its latest calculation involved a large amount of data analysis, focusing on a number of factors including the movements of other aircraft.
Engineers spent all weekend looking back at a previous Malaysian Airlines Boeing 777 flights, going back several weeks.
They compared the satellite data from those flights with flight MH370 and were able to work out it went south.
This is cutting-edge modelling, never tried before. It uses the Doppler effect - which is what makes a police siren sound different from different points.
They had it reviewed by other scientists before handing it over.
As far as they can tell, the plane was flying at cruising height, above 30,000ft. They found no evidence of fluctuating heights being reported.
This is it now - they cannot pinpoint the position any further. They handed this data over on Sunday morning.
It involved an entirely new way of modelling which is why the analysis took some time, the firm said.
A spokeswoman for the AAIB said: "As set out by the Malaysian prime minister, we have been working with the UK company Inmarsat, using satellite data to determine the area on which to focus the search.
"We are not able to comment further on this investigation, which is being led by the Malaysian authorities."
Oceanographer Dr Simon Boxall, from the University of Southampton, told the BBC it was significant that Inmarsat had been tracking satellite data, rather than locations.
"The algorithms and the techniques they've applied to try and locate to within a certain area where the last transmission was made is really quite phenomenal - but also quite tragic because it does show this plane was heading to an open area of ocean."
Dr Boxall continued: "They [Inmarsat] started from scratch. They've probably crammed almost a year's worth of research into maybe a couple of weeks, so it's not a routine calculation they would ever, ever make.
"So they've been looking at all the signals they have, all the recordings they have, and processing that many times over to try and pinpoint where the plane's signal came from. Technologically it's really quite astounding."
He added Inmarsat "wouldn't have released this sort of information without being 100% certain".
'Deep sadness'
Philip Baum, editor of Aviation Security International Magazine, said the mystery of the missing Boeing 777 jet had not been solved.
"We still believe there was a deliberate act that took place on board the flight deck inside the cockpit that resulted in the aircraft turning and heading south," he said.
"Indeed, south of the next landmass would have been Antarctica. So until we find the black box we're really not going to know anything more."
Airline pilot Peter Benn said finding some of the wreckage could help explain what happened to the plane.
He told the BBC: "I don't think anyone should underestimate the magnitude of that task. It is a vast undertaking, suffice to say if some debris can be recovered it would provide an awful lot of clues."
Mr Razak told a news conference in Kuala Lumpur that work by the AAIB and Inmarsat had revealed MH370's last position was in the ocean west of Perth, Australia.
"This is a remote location, far from any possible landing sites. It is therefore with deep sadness and regret that I must inform you that - according to this new data - flight MH370 ended in the southern Indian Ocean," he said.
He added that for the relatives of those on board, "the past few weeks have been heartbreaking. I know this news must be harder still".
Malaysia Airlines said all relatives of those on board had been informed "face-to-face by our top management" at hotels where they were waiting, as well as by text message.
Boeing said in a statement: "Our thoughts and deepest sympathies continue to be with the families and loved ones of those aboard."
Royal Navy ship HMS Echo is due to arrive in the area on Tuesday to help with the search.
BBC News / Washington Post Blog
Airlines News Breaking News Latest News malaysia airlines flight 370 Malaysia News MH370 MH370 found missing MH370