Right-arm fast bowler Woakes has been ruled out of the final Ashes due to recurrence of a side injury.
ESPNcricinfo reports that Woakes had carried a heavy workload in the Ashes series and had run over 35 miles in the field during Australia's innings in Perth, and had been diagnosed with a minor strain on his left side.
The England management decided not to play Woakes. The 28-year-old was out of action for three months in 2017.
Woakes had played every game in the four Ashes and had bowled 48 overs on the slow Melbourne Cricket Ground (MCG) pitch last week.
Meanwhile, Crane will make his Test debut almost a year after playing a single Sheffield Shield game for New South Wales.
At 20-year-old thus will be the youngest specialist spinner to make his Test debut for England in 90 years. Ian Peebles held that record when he made his debut aged 19.
Moeen claimed just three wickets at 135 during the first four Tests.