The near miss, on May 22 near Loch Garry, was categorised as the highest risk by the UK Airprox Board.
The red and yellow Eurocopter AS350 was "barely perceptible" to the Tornado pilot as the cockpit cover of the plane was smeared with dirt, according to the report.
The incident was shortly before 1.30pm in a low level flying training exercise over Dalnaspidal, one mile north of Loch Garry.
The helicopter, which had four people on board, was travelling at the same height of 440ft.
An eyewitness driving north on the A9 told investigators he saw the Tornado travelling south at around the same height as the helicopter before turning right and crossing its flightpath.
It is thought to be the seventh near-miss involving a Tornado in the last three years, although the board noted that the RAF was now fitting collision avoidance systems to its Tornados, which "might reduce the likelihood of a repeat of this type of incident in the near future".
The report stated: "The geometry of the incident meant that it was impossible for the AS350 pilot to see the Tornado overtaking rapidly from his rear quarter so it was agreed that the cause was a non-sighting by the Tornado crew. In light of this cause and the estimated miss distance, the Board unanimously agreed that there had been a risk of collision."