Director of Public Prosecutions Keir Starmer said there is "no realistic prospect" of a conviction after a 15-month inquiry.
He said there is evidence that the officer, a member of the Metropolitan Police's territorial support group, assaulted the 47-year-old newspaper seller.
But he said a manslaughter charge could not be brought because of "irreconcilable" differences between doctors over what caused his death.
And alternative charges of assault or misconduct could not be brought because of the evidence, legal time limits and case law.
Mr Starmer said the evidence of Dr Freddy Patel, who found Mr Tomlinson died of natural causes, could undermine any prosecution.
Dr Patel could be struck off within months as the General Medical Council examines claims that he bungled four other autopsies.
Mr Starmer said the doctor's findings also ruled out one kind of assault charge because it could not now be proven that the strike or push harmed Mr Tomlinson.
He added that the officer could not be charged with common assault, which does not require proof of injury, because there is a six-month time limit.
And prosecutors discounted charging him with misconduct in a public office because of legal precedents.
Reacting with fury to the announcement, Mr Tomlinson's family accused the authorities of a "big cover-up" and pledged to seek a review.
Fighting back tears outside CPS headquarters, his son Paul King called for the officer responsible to be "named and shamed".
He said: "It's outrageous. We feel like it was not a full investigation from the beginning. It's a big cover-up.
"He has just admitted on TV that a copper assaulted our dad. But he hasn't done anything. He's the man in charge ... why hasn't he charged him?
"They knew that if they dragged this out long enough, they would avoid charges. They knew just what they were doing.
"They've pulled us through a hedge backwards - now we have to go on living our lives."
Tomlinson family solicitor Jules Carey labelled the decision "disgraceful" and said an inquiry must examine if it is due to a "lack of will or incompetence".
He said: "Clearly, it is a disgraceful decision. The CPS have accepted the conduct of the officer was unlawful."
Asked what she will do now, Mr Tomlinson's widow Julia said: "What do you expect us to do? What can we do?"
The death of Mr Tomlinson, 47, on April 1 last year became global news after video evidence emerged that challenged the original official version of events.
Police told the newspaper seller's widow and nine children that he died of a heart attack after being caught up in crowded streets around the protests.
But footage later showed Mr Tomlinson being struck from behind by a member of the Metropolitan Police's controversial territorial support group.
Mr Tomlinson was hit by a baton and shoved to the ground by an officer wearing protective clothing. He was also bitten by a police dog.
He died several minutes later after staggering about 100 yards into Cornhill, near St Michael's Alley, and collapsing.
Speaking on the fifth anniversary of the death of Jean Charles de Menezes, Mr Starmer said the three post-mortem examinations were at the centre of the decision.
Dr Patel found he died of natural causes, linked to coronary artery disease, but two other doctors found he died as a result of blunt force trauma, in combination with natural disease.
Dr Patel is facing the General Medical Council (GMC) accused of giving questionable verdicts on four causes of deaths, several of which later turned out to be suspicious.
Mr Starmer said: "After a thorough and careful review of the evidence, the CPS has decided that there is no realistic prospects of a conviction against the police officer in question for any offence arising from the matter investigated and that no charges should be brought against him."
Campaigners were gathering outside New Scotland Yard this afternoon to protest against police violence.
The Independent Police Complaints Commission said it will pass its file to the Met, which will consider if the officer should be disciplined.
An inquest will now examine the circumstances of Mr Tomlinson's death and the case could be reconsidered by prosecutors after it is concluded.
A Metropolitan Police spokesman said the force offered its "sincere regret" over the death of Mr Tomlinson.
He said the officer could still face misconduct proceedings once the force receives the IPCC report.
A spokesman said: "Our thoughts remain with the family of Ian Tomlinson and those affected by his death."
Green politician Jenny Jones, a member of the Metropolitan Police Authority, said: "This is yet another outcome from the CPS that satisfies nobody and does not even satisfy the criteria of natural justice.
"It definitely will not satisfy the family, particularly as it is even too late for the assault charge to be brought against the officer.
"It is not good for the officer either, because he has not been acquitted and has been clearly shown to be someone who behaves aggressively.
"I hope, at the least, the police are going to hold him to account. Misconduct alone is not really enough."
