The Zimbabwe Conservation Task Force said Walter Palmer killed Cecil with a crossbow
Conservationists in Zimbabwe say the man who paid $50,000 (£32,000) to kill the country's most famous lion was an American dentist.
The Zimbabwe Conservation Task Force (ZCTF) named the tourist as Walter Palmer from Minnesota and said he shot the animal with a crossbow and rifle.
The lion, named Cecil, was later skinned and beheaded, the ZCTF said.
Two Zimbabwean men who were involved face poaching charges because the group did not have a hunting permit.
The men - a professional hunter and a farm owner - could be sentenced to up to 15 years in prison in Zimbabwe if they are found guilty. They are due to appear in court on Wednesday.
It is unclear whether Mr Palmer has already returned to the US but Zimbabwean police confirmed that he could also face poaching charges.
"We arrested two people and now we are looking for Palmer in connection with the same case," police spokeswoman Charity Charamba told reporters.
Authorities had previously said that a Spanish tourist may have been behind the killing.
Mr Palmer told the Minnesota Star Tribune that "some things are being misreported". He said he would release a statement later on Tuesday.
A spokesman for the dentist told the Guardian that Mr Palmer thinks "he might have shot that lion that has been referred to as Cecil".
But he said the American "had the proper legal permits and he had hired several professional guides".
The dental practice run by Mr Palmer was closed on Tuesday and a note was placed on the door referring visitors to a public relations firm, according to local press.
The practice's Facebook page was removed from the site after being besieged by angry comments and the company website was also taken down.
Cecil was a major tourist attraction at Zimbabwe's famous Hwange National Park
Zimbabwe, like many African countries, is battling to curb illegal hunting and poaching which threatens to make some of its wildlife extinct.
The 13-year-old lion was a major tourist attraction at the country's famous Hwange National Park.
He is believed to have been killed on 1 July but the carcass was not discovered until a few days later.
The ZCTF said the hunters had used bait to lure him outside Hwange National Park during a night-time pursuit.
Mr Palmer is said to have shot Cecil with a crossbow, injuring the animal. The group didn't find the wounded lion until 40 hours later, when he was shot dead with a gun.
The animal had a GPS collar fitted for a research project by UK-based Oxford University that allowed authorities to track its movements. The hunters tried to destroy it, but failed, according to the ZCTF.
On Monday, the head of the ZCTF charity told the BBC that Cecil "never bothered anybody".
"He was one of the most beautiful animals to look at," Johnny Rodrigues said.
The six cubs of Cecil will now be killed by the new male lion in the pride, Mr Rodrigues added, in order to encourage the lionesses to mate with him.
"That's how it works... it's in the wild. It's nature taking its course," he said.