John Provan, 64, and Elizabeth Allan, 63, from Barrhead were pronounced dead at the scene along with John Leonard Stern, 71, from Bearsden.
Six other people were injured during the crash at the Jim Clark Rally in one of the blackest days for Scottish motorsports.
Police said the fatal crash took place at about 4pm when a rally car came off the road near Kelso, hitting spectators.
Both the driver and the co-driver were uninjured. The car involved was car 7, a Citroen DS3 driven by David Carney of Westport, Co Mayo in Ireland. The co-driver was Ray Fitzpatrick, from Cahir, Co Tipperary.
In another accident two hours earlier, a rally car also hit five people. Four were treated at the scene and another is in a serious condition in hospital. Police Scotland said the rally was cancelled immediately after the fatal crash. Official confirmation of the crashes came almost seven hours after the first collision.
Eyewitnesses to the fatal crash described "terrible" scenes.
Spectator Tony Cowan said: "It was just one car which lost control. It went sideways one way and then to the other side of the road and ploughed in to four people.
"It was terrible, absolutely terrible. I ran to help but there was little I could do. The air ambulance arrived after about three-quarters of an hour. There were police cars and ambulances. It was chaos, just chaos."
Eyewitness Tommy Tait wrote on Facebook: "We must be like cats have nine lives never have we been so close to getting wiped out by a rally car our thoughts go out to the 4 who got hit."
Another spectator also wrote on Facebook: "Huge accident at rally. Not far from us. About 15 emergency vehicles here now and about 40 people stood working on the injured. Not good."
The racing competition takes place over three days on closed roads in the Duns and Kelso areas. It is the only all-Tarmac rally to be held on closed-off public roads in mainland Britain The rally is named after Scottish Formula One driver Jim Clark, who grew up in the area. He was killed in a motor racing accident in Hockenheim, Germany, in 1968.
Local MSP and Scottish Labour leader John Lamont said: "This is tragic news for the Borders, and my thoughts and prayers are with the victims and their families.
"I know that the rally organisers place considerable emphasis on the safety of the spectators and drivers but with any event of this nature, there will always be an element of risk.
"I live just a few miles away from the scene of the accident and I know that everyone is shocked and saddened by this dreadful news."
Scotland's First Minister Alex Salmond said: "This is desperately sad and difficult news from the Borders of the tragic circumstances that have occurred at the Jim Clark Rally.
"The police have confirmed three fatalities and my thoughts are with all of those involved and the families and loved ones of those who have lost their lives. The Government is in contact with Police Scotland and we await the outcome of their inquiries.
"The Jim Clark Rally is a longstanding event of over 40 years. It is much loved in the Borders and by the rally driving community who I know will share in our sadness at what is a black day for the Borders and for Scotland."
The driver of the rally car is understood to have lost control after crossing a bridge on a straight section of the stage before colliding with spectators.
Within minutes, police has cordoned off the area. It is understood a crew member in one of the following cars was professionally medically trained, and immediately administered treatment to the injured spectators.
The site was instantly identified as a "major incident" scene.
The event organisers, the Border Ecosse Car Club and the Berwick & District Motor Club said: "This is a tragic event, and our thoughts are with the friends and families of the people tragically killed and injured in today's incident."
Within a few hours of the incident, a Police Scotland gold commander was at the scene co-ordinating the taking of statements from rally officials.
In the earlier crash, a car suffered steering failure and hit spectators after it entered a field near the village of Eccles.
Motorsports insiders say the fatal crash may prompt calls for the rally to be banned, and will certainly strengthen calls for even greater safety measures to be taken.