Samuel McGhee, 56, of Glasgow, is the second of six people who died in the bar to be named. The three helicopter crew members were named on Sunday.
Rescuers are now aiming to lift the helicopter wreckage from the roof and have said they cannot rule out the possibility of more bodies being found.
The helicopter crashed into the pub at about 22:25 GMT on Friday.
Deputy Chief Constable Rose Fitzpatrick, speaking at the crash scene early on Monday morning, said: “I can confirm that sadly a further body has tonight been located and removed from the scene.”
She added: “Efforts are ongoing as we speak to establish the identity of the latest fatality.”
And, naming Mr McGhee, she said: “Our thoughts are with his family and friends tonight as they are with all those affected by this tragedy.”
Police Scotland's “absolute priority has been to locate the bodies of people who were within the pub at the time of the incident and recover them safely”, she added.
“This process takes time as formal identification procedures have to take place before we can notify relatives and publicly confirm identities.”
She said work would go on “throughout the night to stabilise the scene in order to continue to progress the search and recovery”.
On Sunday, police named three dead helicopter crew as pilot David Traill, 51, and Police Constables Kirsty Nelis, 36, and Tony Collins, 43. The first victim to be named was pub-goer Gary Arthur, 48, of Paisley.
Of the 32 people who were injured in the crash, 12 remain in hospital. Three of these casualties were being treated in intensive care, where their conditions were described as serious but stable.
The family of Mark O'Prey fear he may be one of the victims still buried under the rubble.
His father Ian and sister Louise spent much of Sunday at the crash site waiting for news.
Ms O'Prey told BBC Radio's Good Morning Scotland programme of the family's frustration at the time it has taken to remove the wreckage.
“There is terrible things going through my head about what kind of state he's in and we want to get him back intact,” she said.
“We are pretty sure that he's gone but until I get that information we just don't know when that's going to be.
“I can't accept it until then. But there's still that glimmer of hope that they might bring people out alive, even though they are telling us that there is nobody in there alive.”
The Scottish Fire and Rescue Service said heavy equipment was brought in on Sunday, and the three-tonne helicopter had been secured to prevent it sinking further into the building.
The aim is now to prepare the rest of the aircraft for lifting during daylight hours on Monday.
ssistant chief officer David Goodhew told BBC Scotland: “That has allowed our urban search and rescue teams to actually tunnel under the helicopter without fear of it falling any further onto them.
“The helicopter is extensively damaged, but certainly the Air Accident Investigation Branch, who are in charge of lifting the helicopter, want to preserve the evidence.
“They want to make sure that they have absolutely all of the information, and they would like to get the largest part of the helicopter out in one piece.”
The officer described conditions inside the pub as “dreadful”, with crews working in extremely confined spaces.
He added: “As they tunnel into the building they have to make sure that it is safe, and that there is not going to be any further collapse onto these people.
“So as they go into the building they have to shore it up to make sure that the helicopter doesn't sink and further parts of the building don't fall on rescue crews.”
Scottish Fire and Rescue Service chaplain, The Reverend Gordon Armstrong, said: “It's just a very difficult situation. We can imagine what's happening there.
“I haven't seen inside but just listening to the messages, it's just one of those situations we just can't speed up.
“It can only go at the pace of the experts and we need the experts in this situation.”
Scotland's Deputy First Minister Nicola Sturgeon told BBC Scotland firefighters were working as quickly and safely as possible.
“I know that those in the air accident investigation side of this have described this as one of the most complex sites that they've ever worked on,” she said.
“It's important that the helicopter is removed in a way that firstly preserves the dignity of the victims inside the pub, but secondly doesn't impose any unnecessary risks on the people carrying out this work.
“I fully and completely understand the frustration and the anguish for people who are waiting for news.”
Sections of the rotor blades were hoisted away from the roof on Sunday.
Once the helicopter has been lifted it will be moved to a secure site for detailed investigation.
Aviation expert Chris Yates told the BBC it was not yet clear if the helicopter had a black box flight recorder but said investigators may be able to establish the cause of the crash without one.
“This is a police helicopter,” he said. “There is all sorts of surveillance on board the helicopter.”
“There is all sorts of data collection equipment as well so there is an awful lot that the investigators can probably go on to understand what went wrong on Friday night.”
The Clutha, in Stockwell Street on the banks of the River Clyde, was packed with about 120 people listening to live music when the helicopter crashed into it.
Eyewitnesses outside described how the aircraft “fell like a stone” from the sky.
Others described how passers-by formed a human chain to help get people out of the pub.
Officers from Police Scotland's major investigations team have asked for any footage of the incident to be emailed to: email@example.com
In a separate inquiry, the Air Accidents Investigation Branch (AAIB) is trying to establish what caused the crash.
Its team is being assisted by experts from Eurocopter, which manufactured the EC135 T2 aircraft.
Within the city, efforts continue to help survivors and the bereaved.
Glasgow City Council said it had put measures in place to provide financial assistance to victims of the incident.
Charitable funds administered by the council will be made available to support anyone facing hardship as a result of the tragedy – including casualties and the families of those who lost their lives.
The council said it was already in contact with some of those affected by the incident – and will announce further details of how help will be made available.
The actor Colin McCredie, best known for his role in TV drama Taggart, has also said he plans to organise a concert to raise money for victims and their families.