Detective Constable Adele Cashman, 30, who was based at Kentish Town in North London, was in pursuit of a man yesterday evening when she suddenly collapsed.
The incident took place in Belsize Park Gardens in the Camden area after a 59-year-old woman reported that her smartphone had been snatched out of her hand.
Uniformed officers, who were on duty in the area saw the chase and joined in, while DC Cashman requested more help.
DC Cashman, who was a response team officer, was taken by ambulance to the Royal Free Hospital in nearby Hampstead but was pronounced dead at 9.10pm.
Her family were informed of her death and an investigation has been launched into the circumstances.
Paying tribute to the officer, Commander Tony Eastaugh said: "The thoughts of everyone in the Metropolitan Police Service are very much with Adele's family, friends and colleagues at this extremely difficult time.
"Adele worked on both Camden and Wandsworth boroughs and was held in high regard by all who met her - she will be sorely missed by everyone who had the privilege of working alongside her."
A 17-year-old boy was arrested close to the scene of the incident, while a second boy, also 17, was later detained and a phone recovered, Scotland Yard said.
The suspects were in custody at north and central London police stations, a spokesman for the force said.
Acting Borough Commander Richard Tucker, from Camden Police, said: "Adele was a much-loved and wholly dedicated officer.
"We at Camden are completely devastated at her sudden passing and our thoughts and prayers are with her family and friends at this tragically sad time."
DC Cashman joined the force in 2006 and was stationed at Wandsworth Borough, where she worked as a police constable.
She transferred to Camden in 2010 as a detective.
A post-mortem examination was due to take place today.