The draw was made on Monday evening by former Magpies manager Ruud Gullit - who took Newcastle to the final in 1999 - and ex-England international Paul Ince.
Newcastle faced Blackburn on Tyneside at the same stage in 2011/12, with Hatem Ben Arfa scoring a memorable solo goal.
In total, the sides have met 11 times in the competition (including replays), with Newcastle winning six and losing just twice.
Most famously, United beat Rovers after a replay at the semi-final stage in 1951/52, before defeating Arsenal in the final.
The game could mean a return to St. James' Park for Adam Armstrong, who joined the Lancashire club in the summer following a successful loan spell last term. The England under-21 international - a product of the club's Little Benton Academy - made 21 appearances for Newcastle in all competitions.
Third round ties are set to be played over the weekend of Saturday, 5th January 2019.
United were handed a home tie against Luton Town at the third round stage last term, beating the then-League Two side 3-1 before exiting the competition at the hands of eventual cup winners Chelsea.