Neil Warnock's men will make the long trip south for a Third Round tie over the weekend of 9-10 January. Further match details will be announced in due course.
It'll be the second meeting between the two sides in TW8 this campaign following our 0-0 draw in the Sky Bet Championship three weeks ago.
The 1997 runners-up currently sit tenth in the second tier, having only been past the Fourth Round once in the past five years. Last year saw Thomas Frank's side reach the Last 32 before bowing out to Premier League side Leicester City at Griffin Park.
We've met Boro four times previously in the World's oldest cup competiton, winning three of those meetings. As a then Southern League First Division side, we beat top flight Boro 1-0 in the Second Round back in 1907. We also beat The Teessiders on our way to the Quarter-Final back in 1948/49.