Dr Richard Field, 49, and Dr Lina Bolanos, 38, were found dead in the apartment in Boston, Massachusetts, on Friday night.
During his final moments Dr Field had texted a friend to report a "serious situation" with a gunman in his home, according to the Suffolk County District Attorney's Office.
Police were alerted at 8.40pm and they entered the 11th-floor apartment using keys found on the floor outside the victims' door.
They found the suspect during a search and fired multiple shots believing he was armed.
Police found a backpack containing jewellery, a replica firearm and at least one knife in the apartment, according to the district attorney's office.
Bampumim Teixeira, 30, was charged with two counts of murder on Monday from his hospital bed where he was being treated for three gunshot wounds.
According to reports Dr Field was born in Hammersmith, west London, and the Massachusetts medical register said he graduated from Sheffield University's medical school in 1999.
The North Shore Pain Management centre, where he had worked since 2010, spoke of him as a "guiding vision" who gave patients and colleagues his "tireless devotion".
"His tragic and sudden passing leaves an inescapable void in all of us," the centre added in a statement.
Paying tribute, one patient wrote on Facebook: "He was an amazing Dr. who was so kind and compassionate.
"I always said if he ever moved back to England I would follow him. Dr Field changed my life."
The Foreign & Commonwealth Office has not confirmed his nationality.
Dr Bolanos worked at Massachusetts Eye and Ear hospital as a paediatric anaesthetist and was an instructor at the Harvard Medical School.
John Fernandez, the hospital's president, said: "Dr Bolanos was an outstanding paediatric anaesthetist and a wonderful colleague in the prime of both her career and life."
The suspect, of nearby Chelsea, had recently been released from jail, having passed notes demanding money from a bank on two occasions, according to prosecutors.
Teixeira's lawyer, Steven Sack, entered not-guilty pleas to the two counts of murder at South Boston Municipal Court and did not request bail.
The case returns to court on June 8.