Germany will be the home nation for the 17th European Football Championship, which kicks off in June
City's domination of the first half was absolute and the only surprise was it took a penalty for them to lead at halftime, De Bruyne slotting home in the 37th minute.
Newcastle did improve marginally after the break and substitute Dwight Gayle somehow missed a gaping goal.
One minute later Sterling curled home a delightful effort to seal City's progress and set up a semifinal against Arsenal.
All four of this year's Cup quarter-finals, all played behind closed doors, were won by the away team - the first time that has happened since 1987.
Manchester United will face Chelsea in the other semifinal.
Manchester United v Chelsea
Arsenal v Manchester City
Matches will be played at Wembley on July 18-19
Germany will be the home nation for the 17th European Football Championship, which kicks off in June
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