Nick Wharton from East Sussex was running in a wood on the Hooke Estate near his home when the branch fell from an oak tree.
A post-mortem examination found he died from multiple injuries, including serious chest trauma, after being hit on the back by the falling branch.
Wharton was a probationary PC based at Belgravia police station and training for the London Marathon when he was hit by the branch on 11 September 2009.
At an inquest into his death Superintendent Simon Ovens paid tribute to the 30-year-old: "Nicholas was an outstanding young officer. He had already made a big difference to the lives of people Westminster and he had a really bright future in the Met. The force will be a poorer place without him."
Tree surgeon Simon Birkby told the inquest the 200-year-old oak was diseased but it was "incredibly uncommon" for lethal branches to fall to the ground without warning.
He said: "Everything has a life span. But it is unfeasible to check the safety of every tree by every public footpath."
East Sussex deputy coroner Kate Palmer said there was no evidence of gross negligence by landowner James Tillard and recorded a verdict of accidental death.