The attacker pulled up next to a stationary police van on the busy Paris street before opening fire, killing one officer immediately.
He then tried to run along the pavement as he continued firing, injuring two further officers and a female tourist before authorities opened fire, killing the attacker.
Paris Prosecutor François Molins said the gunman has been identified and authorities are still trying to determine whether he had any accomplices.
The suspect was reportedly already known to police after he was identified from papers left in his car.
Police have raided the home of a 39-year-old man in an eastern suburb of Paris in connection with the shooting.
A police document seen by the Associated Press identifies the address of the raid in the Chelles neighbourhood of the capital as the family home of Karim Cheurfi, a 39-year-old previously convicted of attacking police.
In 2001, the suspected terrorist opened fire on two police officers after he was caught in a stolen car, resulting in serious injuries.
He was sentenced to 20 years in a high security prison in 2003, but was released early following an appeal ruling.
Meanwhile, an arrest warrant has been issued for a second suspect who is believed to have arrived from Belgium by train.
French President Francois Hollande said he was convinced the shooting was “terrorist-related” moments before ISIS claimed responsibility for the attack.
One eyewitness said a man got out of a car and began shooting “with a Kalashnikov”, hitting a policeman.
The police union said the officer was killed in car while stopped at a red light with the attacker driving by.
Witness Chelloug, a kitchen assistant, told Reuters: “I came out of the Sephora shop and I was walking along the pavement where an Audi 80 was parked. A man got out and opened fire with a kalashnikov on a policeman.
“The policeman fell down. I heard six shots, I was afraid. I have a two year-old girl and I thought I was going to die… He shot straight at the police officer.”
French interior ministry spokesman Pierre-Henry Brandet said: “An automatic weapon was used against police, a weapon of war.
Mr Brandet said the shooting started shortly after 9pm local time when a car stopped alongside a stationary police car.
He said: “A man immediately got out and opened fire on the police car, fatally wounding a police officer … He also wounded a second one, it would seem very seriously.”
Mr Brandet added the “terrorist threat” in France remains high.
President Francois Hollande said: “We are convinced of one thing. The potential leads that will lead us to the truth are of a terrorist nature.
“The counter terrorism division of the public prosecutors office has been mobilised and an investigation will be carried out.
“We will be extremely cautious, extremely careful, especially as this is an election period.”
He will hold a security cabinet meeting on Friday morning.
Mr Hollande added: “We all need to realise that our security forces, our law enforcement forces are targeted. They are doing tremendous work and they have the full support of the nation.
“This is a message for everyone. You will be protected. All the measures that could have been taken, have been taken.
“I am deeply sad tonight and I would like to express my heartfelt condolences for the policeman who was gunned down for his family.
“I would like to say that we do everything we can to counter terrorism.”
Mr Hollande said security sources will be of the utmost vigilance during the election as a result of the shooting.
French Interior Minister, Matthias Fekl, took to Twitter to pay tribute to the killed policeman and those wounded in the attack.
He wrote: “Tributes to the killed policeman and injured police officers, thoughts are with the relatives. In the face of terrorism, the nation is united with the law enforcement.”
Police warned people to avoid the area with residents evacuated from nearby buildings as the investigation got underway.
Mr Brandet said police officers were deliberately targeted in the Paris Champs Elysees avenue shooting, but it is too early to say what the motive was.
Police sources had said earlier that the shooting could have been an attempt at an armed robbery.
The Paris prosecutor’s office says the counter-terrorism office has opened an investigation into the shooting.
Local media reported gunfire shortly after 9pm local time in the French capital.
Meanwhile Anne Hidalgo, the Mayor of Paris, has also spoken out about the attack.
She tweeted: “Tonight, a terrorist blinded by hatred and death, has ended the life of a police officer and injured two of his colleagues.
“I extend my condolences to the family and relatives of the police officer who was killed in the line of duty.
“I also wish a speedy recovery to his two colleagues and a tourist who was injured.
“I salute the dedication, bravery and professionalism of the police and rescue forces.
“We won’t give in, and remain United in the face of this odious and insidious threat that weighs on our cities.”
The entire area, a haven for tourists, was put on lockdown as armed police secure the Champs Elysees.
The UK Foreign Office said: “The British Embassy is in contact with local authorities and urgently seeking further information following reports of a shooting incident on the Champs-Elysees in Paris.
“You should remain vigilant and follow the advice of the local security authorities and/or your tour operator.
“If you’re in the area and it is safe to do so, contact your friends and family to tell them you are safe.”
Local metro stations were shut down as police continue to search for the second attacker.
The shooting comes just a few days before France’s presidential election with the 11 French presidential candidates currently taking part in a TV debate around three miles from the scene.
French presidential candidates Francois Fillon and Marine Le Pen have cancelled Friday’s campaign events in the wake of the shooting.
Voters are set to head to the polls on Sunday in the first round of a two part election, and campaigning was due to be wrapped up on Friday.
Mr Fillon had been scheduled to go to the French Alps for a campaign event but told France 2 television he would not go.
The attack occurred near 78 Champs Elysee – close to several major chain stores including Nike and Apple, which are popular with tourists.
US president Donald Trump said: “My condolences to the people of France, again, its happening, it seems. I just saw it as I was walking in.
“That’s a terrible thing and that’s a very, very terrible thing that’s going on in the world today.
“It looks like another terrorist attack. What can you say, it looks like it never ends.
“You have to be strong and you have to be vigilant and it’s been happening for a long time.”
Socialist candidate for the French election, Benoit Hamon tweeted: “My thoughts are with the police, complete support with the police against terrorism.”
The metro station Franklin Roosevelt, close to l’Arc-de-Triomphe has been closed.
The Front National politician Florian Philippot tweeted: “Thoughts are with the police officer who was killed tonight in Champs Elysee and thoughts for his injured colleague. Horror yet again.”
France remains on high alert following the 2015 Paris attacks.
The shooting comes just two hours after a police lockdown on Rue de Rivoli – a nearby street in the heart of the city.
The Paris Metro was suspended at the station on the street as officers sealed off the road.
It is not yet known whether the street closure and the shooting are linked.
France has lived under a state of emergency since 2015 and has suffered a spate of Islamist militant attacks that have killed more than 230 people in the past two years.
Earlier this week, two men were arrested in Marseille whom police said had been planning an attack ahead of the election.
A machine gun, two hand guns and three kilos of TATP explosive were among the weapons found at a flat in the southern city along with jihadist propaganda materials according to the Paris prosecutor.