Armed officers attempted to stop a vehicle in Stratford, east London, early on Saturday morning.
They followed the car to Ashlin Road in Newham, where 37-year-old PC Gary Toms was critically injured.
Pc Toms, who joined the force in January 2002, has been described as a "dedicated officer" who was known for his "professional attitude".
Ch Supt Bill Tillbrook, in charge of the Met’s Specialist Firearms Command, said: “My deepest sympathies go to Gary’s family, friends and colleagues at this distressing time. Gary was a dedicated officer who died doing the job he had trained to do. He was a hard working police officer who was known amongst his colleagues for his sense of humour and professional attitude.”
The Commissioner, Sir Paul Stephenson said: "This is especially poignant news given that Gary died on the 25th anniversary of Yvonne Fletcher's death.
"It shows us all that the potential dangers officers face when doing their duty are never far away.
“To lose such a young and promising officer is the most tragic of losses for his family - my most sincere condolences to them. This is also a loss that the wider Met family should not, and never will, forget."
I don't know if we ever met in a professional capacity, but that doesn't matter, my thoughts go out to his colleagues, friends and families. I was following the story since Sunday and hoping that he would recover.
