Some 59 people were also injured when the blast caused by an improvised explosive device carried by the attacker detonated at the Manchester Arena.
Announcing that the death toll had risen, Greater Manchester Police chief constable Ian Hopkins said: “What I can confirm is that there are children among the deceased.”
He said: “This has been the most horrific incident we have had to face in Greater Manchester and one that we all hoped we would never see.
“Families and many young people were out to enjoy a concert at the Manchester Arena and have lost their lives.
“Our thoughts are with those 22 victims that we now know have died, the 59 people who have been injured and their loved ones.
“We continue to do all we can to support them.”
Mr Hopkins said a “fast-moving investigation” had established the attack was conducted by one man, although detectives are working to establish if he was “was acting alone or as part of a network”.
“The attacker, I can confirm, died at the arena.
“We believe the attacker was carrying an improvised explosive device which he detonated, causing this atrocity.”
Police were called to reports of an explosion at the Manchester Arena at 10.33pm, shortly after US singer Ariana Grande had finished her performance.
Victims described being thrown by the blast that scattered nuts and bolts across the floor.
More than 240 calls were made to the emergency services, with responders including 60 ambulances flooding the area.
More than 400 police officers were deployed as part of the operation, with a visible presence remaining on the streets of Manchester on Tuesday.
The dozens of victims injured in the attack are being treated at hospitals across Greater Manchester, and a hotline has been set up for those with concerns over loved ones who remain unaccounted for.
A large cordon remains in place around the arena and nearby Manchester Victoria Station, which was evacuated during the incident and remains closed, while forensic investigators gather evidence.
Police have appealed for concert-goers and witnesses to provide police with footage from the scene if they believe it can assist the probe.
Meanwhile anyone who witnesses suspicious activity is urged to report it to the anti-terrorist hotline.
Witnesses reported hearing a “huge bang” at around 10.30pm, as fans were leaving the arena shortly after the show finished.
One fan, Majid Khan, 22, described how the explosion happened: “A huge bomb-like bang went off that hugely panicked everyone and we were all trying to flee the arena.
“It was one bang and essentially everyone from the other side of the arena where the bang was heard from suddenly came running towards us as they were trying to exit.”
Oliver Jones, 17, who attended with his 19-year-old sister, said: “The bang echoed around the foyer of the arena and people started to run.
“I seen people running and screaming towards one direction and then many were turning around to run back the other way.”
The area around the arena was swamped with police and emergency services and approach roads were closed.
Ms Grande, 23, has said she is “broken” following the explosion moments after she left the stage on Monday evening.
Tweeting in the early hours of Tuesday, the 23-year-old said: “broken. from the bottom of my heart, i am so so sorry. i don’t have words.”
Meanwhile Grande’s management team, Scooter Braun Projects, said they had been left heartbroken by the incident and praised the actions of Manchester’s emergency services.
They said: “Words cannot express our sorrow for the victims and families harmed in this senseless attack.
“We mourn the lives of children and loved ones taken by this cowardly act.
“We are thankful for the selfless service tonight of Manchester’s first responders who rushed toward danger to help save lives.
“We ask all of you to hold the victims, their families, and all those affected in your hearts and prayers.”
A spokesman for the singer had earlier said she had been uninjured in the incident.
Manchester’s Victoria station, which backs on to the arena, was evacuated and all trains and trams cancelled.
Meanwhile the ambulance service warned people only to call “for life-threatening emergencies” and said a “large number of resources” were at the incident.
Manchester Fire and Rescue described the incident as “utterly heartbreaking” and asked people not to dial 999 “unless you really need us”.
Manchester Arena said the explosion happened “outside the venue in a public space”.
“Our thoughts and prayers go out to the victims,” it said.
Sir Richard Leese, leader of Manchester City Council, said: “This is an absolutely horrifying incident and our thoughts are with everyone affected, especially those who have lost loved ones or been injured and traumatised.”
Politicians send condolences
Scotland’s First Minister Nicola Sturgeon tweeted: “Heartbreaking news from Manchester. My thoughts are with all those who have lost loved ones or been injured in this barbaric attack.”
Labour leader Jeremy Corbyn said his thoughts were with all those affected by the “terrible incident” in Manchester.
His political rival Tim Farron, the Liberal Democrat leader, condemned the “shocking and horrific” attack targeting youngsters at the Ariana Grande concert.
In a message on Twitter Mr Corbyn said: “Terrible incident in Manchester. My thoughts are with all those affected and our brilliant emergency services.”
Mr Farron said: “This is a shocking and horrific attack targeting children and young people who were simply enjoying a concert.
“My deepest sympathies are with the victims, and with families who have lost loved ones, as well as those desperately waiting for news.
“I would like to pay tribute to the bravery and dedication of the emergency services.
“This is an attack on innocent people and the nation is united both in its grief and its determination to stand up to this deplorable attack.”
Liverpool’s metro mayor Steve Rotheram, whose daughters were at the Manchester Arena concert, said: “Feel sick to think that people have lost their lives at a gig attended by so many young people.
“All my thoughts go out to those parents waiting to hear of the safety of their children. It’s a parents worse nightmare. So, so sad.”
Mr Rotheram thanked the taxi driver who picked up his two girls from the venue.