The draw was made at the Etihad Stadium, home of holders Manchester City, by former City defender Micah Richards and ex-Arsenal skipper Tony Adams, on Monday evening.
League One Rochdale and National League North Boston played out a 0-0 draw at Spotland at the weekend, and will meet again in a replay later this month.
The winners of that game will host the Magpies. Ties are set to be played between Friday 3rd and Monday 6th January. Newcastle have never played against either side in the FA Cup, while Rochdale are one of eight current members of the Football League who the Magpies haven't met in a competitive fixture.
Newcastle have never played against Boston in a competitive fixture either, although there have been a handful of friendly and war time matches against both teams.
Last term, United faced Blackburn Rovers at the third round stage, with the Magpies running out 4-2 winners in the replay at Ewood Park after a 1-1 draw at St. James' Park. However, the Magpies were beaten 2-0 at home by Watford in the next round.
All Emirates FA Cup third round ties will be delayed by one minute as part of a Football Association campaign to encourage fans to 'Take A Minute' to think about looking after their mental health, as part of the Heads Up campaign.
The move will see all 32 ties (excluding replays) kick off one minute later than their traditionally scheduled broadcast and non-broadcast timeslots.
The Heads Up campaign aims to harness the influence and popularity of football to encourage more people - particularly men - to feel comfortable talking about and taking action to improve their mental health, to recognise mental fitness as being just as important as physical fitness, and to draw attention to the simple steps that can be taken to look after mental health and wellbeing.
Ticket details will be announced in due course.