Detectives say significant efforts were made to conceal the body, which was discovered on Tuesday night.
Alice's family have been informed. Formal identification is yet to take place and a post-mortem examination is due to be held later, police said.
Convicted murderer Arnis Zalkalns, 41, from Latvia, remains the prime suspect.
He was filmed cycling along the Grand Union Canal 15 minutes after Alice had walked along it, on 28 August. It is the last known sighting of the 14-year-old.
The body was found in the nearby River Brent.
Mr Zalkalns has been missing from his Ealing home since 3 September.
Speaking outside Scotland Yard earlier, Commander Graham McNulty said: "We are unable to make a formal identification at this stage, but clearly this news is devastating for everyone involved in the search for Alice.
"At this time my thoughts are with Alice's family and friends."
He urged anyone with information to come forward, saying it was not too late.
"I would like to thank the local community of Ealing who have shown huge support and patience during the course of our investigation. This discovery will have a significant impact throughout the borough," Cdr McNulty said.
"You only need to walk around the surrounding streets to see the effect that Alice's disappearance has had on the whole community."
Lauren Turner, BBC News
Two women, dressed in black save for the yellow ribbon that has served as a symbol of hope for Alice Gross, walk down Hanwell's Greenford Avenue as they carry out a sombre task.
One has tears in her eyes as she methodically rips the pieces of paper from lampposts and trees - the missing posters bearing Alice's image.
For this community, which rallied together in the wake of the teenager's disappearance, the discovery of a body in the River Brent has cast the darkest shadow.
In a local supermarket, the talk has been about the sadness everyone feels at the latest development.
The shopkeeper said: "I feel very very sad. Especially for her mum.
"I am a mother too - I have a 14-year-old boy. I really feel for her."
Grief in Hanwell as body found
Cdr McNulty read the statement out at 06:30 BST.
BBC News reporter Jon Brain, who was at Scotland Yard, said: "The body hasn't been identified yet but you can be rest assured that detectives would not be holding a press conference at this time of day if they weren't absolutely convinced that it is Alice's body."
He added detectives' main priority now is to find Mr Zalkalns and to ask him about his movements on that day and what he knows about Alice's disappearance and possible murder.
The family's local MP, Stephen Pound, who lives near to the family in Hanwell, said there was an "an incredible sense of sadness"
He said there was also "anger that we're dealing with a pretty cold, cunning predator here - someone who has concealed a body in a particularly effective way.
"This is a pretty horrific business but now - our thoughts have to be with the family."
Alice's disappearance sparked what the Met said was its largest inquiry since the 7/7 bombings in 2005.
Hundreds of officers from several forces around the country have helped with the investigation. The RAF and London Fire Brigade have also been involved.
A dedicated team of 30 officers have scoured hours of footage from hundreds of CCTV cameras.
The Met's homicide and major crime squad took control of the hunt on 3 September.
Two men were arrested in the week after Alice went missing but both were released with no further action to be taken.
On 22 September a knife was discovered in the water and Scotland Yard is awaiting the results of forensic analysis.
A reconstruction of Alice's last known movements was staged last week.
Mr Zalkalns, who has been missing for nearly a month, was convicted of his wife's murder in 1998 and served seven years in jail before moving to the UK in 2007.
The investigation came under fire amid claims of delays in identifying the Latvia-born suspect as a risk, while detectives later admitted they have no power to arrest him if he has managed to flee abroad.
The Met said this was because there was not enough evidence to apply for a European Arrest Warrant (EAW), which extends powers of arrest to foreign police forces.  The discovery of a body has not immediately changed that, it added.
For the warrant to be issued, police would need to have enough evidence to allow someone to be charged. Detectives have said they are not "charge-ready" and want to interview Mr Zalkalns.
The disappearance of teenager Alice Gross is now being treated by police as a murder inquiry after a body was found in a west London river.