Nine other people were injured during the standoff at the Planned Parenthood clinic, which lasted five hours before the suspect surrendered.
A number of people were trapped inside the building as shots were exchanged.
The motive remains unclear. The Planned Parenthood group has drawn anti-abortion protests in the past.
Colorado Springs Police Department identified the suspect as Robert Lewis Dear, from North Carolina.
“I want to convey to the loved ones of the victims, this is a terrible, terrible tragedy that occurred here in Colorado Springs today,” Mayor John Suthers told a news conference.
“Obviously, we lost two civilian victims. We mourn the loss of a very brave police officer.”
The dead policeman was named as Garrett Swasey, 44, who was married with two children.
President Barack Obama said: “We have to do something about the easy accessibility of weapons of war on our streets to people who have no business wielding them. Enough is enough.”
He has previously expressed his frustration after other fatal shootings about not being able to do more on gun control.
Colorado Springs Police Chief Peter Carey said five police officers were among the injured, who were being treated in local hospitals.
Police had sealed off streets around the centre as officers tried to make contact with the suspect.
“We did get officers inside the building,” police Lt Catherine Buckley said.
What is Planned Parenthood?
- A healthcare non-profit-making group with 59 affiliates and 700 clinics around the US
- The largest single provider of abortion in the US
- Its clinics provide many other healthcare services including cancer screening
- Dates back to 1916 when social activist and nurse Margaret Sanger opened the first birth control and family planning centre in Brooklyn, New York
- In the 1960s and 1970s, Planned Parenthood affiliates were at the fore of many court fights to make abortion legal
“They were able to shout to the suspect and make communication with him and at that point they were able to get him to surrender and he was taken into custody.”
Police said the suspect had been seen carrying “some bags” into the building and teams were combing the area for possible explosives.
The suspect’s car which was found nearby was also being checked for explosives, CNN reported.
The manager of a nearby hair salon, Denise Speller, said she had heard as many as 20 gunshots in under five minutes.
She told a local newspaper she had seen one of two police officers appear to fall to the ground and the other attempt to get the wounded officer behind their police vehicle.
Police had told shoppers at a nearby centre to stay indoors.
In a statement, Planned Parenthood said it was not yet clear “if Planned Parenthood was in fact the target of this attack”.
“Our concern is for the safety of our patients, staff and law enforcement,” said itsCEO, Vicki Cowart.
Planned Parenthood has been the focus of protests recently after an anti-abortion organisation secretly recorded a Planned Parenthood official discussing how to obtain aborted foetal tissue for medical research.
Pro-life advocates say this proves Planned Parenthood is selling foetal parts for profit – which is illegal – but this is disputed by the organisation.
New York’s city police said it had deployed critical response vehicles to Planned Parenthood sites in the city because of the Colorado incident, but said there was no threat in the city.