Police have said that the suspect was known to the victims, who were both anesthesiologists. Police, who weren't hurt, fired back and hit him several times.
Prosecutors said a backpack filled with jewelry was conspicuously left at the crime scene.
Field had also worked as an attending pain physician and director of anesthesia for plastic surgery at Brigham and Women's Hospital.
"As doctors, they dedicated their professional lives to alleviating suffering and ensuring the safety of those most vulnerable - children undergoing surgery", the family said.
Another resident, Marisa Richards, says she was surprised because of the building's security. He added that at least one knife was found at the scene. Authorities say that friend called 911 on Friday. The doctor had apparently texted his friend and told the friend to summon help.
The couple were found dead in the apartment having suffered "obvious trauma", the Suffolk County District Attorney's office said.
His body, and his fiance's, would be found by a SWAT team during a protective sweep of the building after the shootout between the gunman and police. A replica firearm or BB gun was also in the bag, Conley said.
Authorities have not said how the doctors died. Teixeira was held without bail. His attorney entered not-guilty pleas for him. However, according to local media reports, he was born in Hammersmith, west London, and the MA medical register said he had graduated from the University of Sheffield's medical school in 1999.
According to CBS Boston, a judge charged 30-year-old Bampumim Teixeira on two charges of murder at Tufts Medical Center.
Bampumim Teixeira, who was arraigned Monday afternoon for the murders of Dr. Lina Bolanos, 38, and Dr. Richard Field, 49, was employed by Palladion Services, a security and concierge company.
Teixeira started firing his weapon when officers got to the condo door, police said. A probable cause hearing has been scheduled for June 8, reports The Boston Herald. He has injuries that are not considered life-threatening.
Dr Bolanos worked at Massachusetts Eye and Ear hospital as a paediatric anaesthetist and was an instructor at the Harvard Medical School. A motive for the murders has not been released. It could not be determined if he has a lawyer. When officers arrived at about 8:40 p.m. Friday, a man immediately started shooting at them, prompting police to return fire.
Field and Bolanos were brutally murdered.
"Dr. Field was a guiding vision at North Shore Pain Management and was instrumental in the creation of this practice", the statement reads.
During the break-in, Dr Field texted a friend to report "a gunman in the house" and seek assistance, police said. It was unclear whether he had obtained an attorney.
This undated photo provided by the Eye and Ear shows Dr. Lina Bolanos, who was found dead with Dr. Richard Field, May 5, 2017, by police at the Macallen Building in South Boston.
Police believe they knew the killer, who made it all the way up to their 11th floor apartment seemingly just to kill them.