Dave Watson's side beat local rivals Sunderland last week to book their place in the last eight of the competition.
And on Thursday night, Spurs beat Norwich 2-0 with with Kazaiah Sterling scoring both goals in the first half.
Now the North London side will travel to St. James' Park on a date to be confirmed. All quarter-final ties must be played by Saturday, 25th February.
When Newcastle last reached the same stage two years ago, they played eventual winners Chelsea in front of 11,664 at St.James' Park.