The body of Valerie Warrington, 73, was found a short time later at an address in the village of Bourton-on-the-Water, which is about 15 miles from Cheltenham.
Gloucestershire Police said detectives were linking the two killings and a man from Cheltenham was arrested on suspicion of murder near the scene and is in custody.
The force confirmed the victims and suspect were known to one another and officers are not seeking anyone else in connection with the deaths.
Superintendent Roddy Gosden said: “At around 6.25am today, emergency services received a call to Sherborne Place in Cheltenham, with a report of a serious assault.
“Officers arrived to find a man in his 60s with stab wounds. He was declared dead at the scene by paramedics.
“Following concerns for the welfare of a second person, officers visited a property in Whiteshoots Hill in Bourton-on-the-Water. They discovered the body of a woman in her 70s who had also suffered stab wounds.”
He added: “Family members have been informed and our thoughts go out to them at this devastating time. They are now receiving support from specially trained officers.”
Police cordons are expected to remain in place at a number of locations over the coming days.
Meanwhile, detectives are appealing to anyone who might have information which could assist their investigation to come forward.
Supt Gosden added: “This has been a challenging situation and we will be providing support to officers and all those who have been impacted by these incidents.
“Understandably people will be shocked to hear that two lives have been lost in such a tragic way.
“Over the coming days, officers will be in the local communities to provide reassurance and we would encourage anyone with concerns to speak to us.”
Anyone with information, particularly those who may have dashcam or CCTV footage of the two areas, are urged to get in contact with police on 101, quoting incident 57 on March 2, or via Gloucestershire Police’s website.