The 18-year-old was driving at almost twice the 30mph speed limit when he hit a car in Manchester in September last year, killing driver Kulwant Singh and his sister, front-seat passenger Ravel Kaur.
Ms Kaur's two sons were also injured in the collision, which happened at the junction of Great Ducie Street and Sherborne Street in central Manchester.
Judge Martin Steiger QC sentenced Meppen-Walter to two 16-month terms, which will run concurrently, and also banned him from driving for three years.
Meppen-Walter wept in court as sentence was passed and Gwyn Lewis, defending, said the England youth international was "truly sorry" for what he had done.
City had twice included Meppen-Walter among their substitutes for Champions League matches, though he had yet to make his debut for the senior team.