The Robins will host the Premiership side in the fourth round of the FA Cup, their reward for beating Championship club Coventry City at the previous stage.
Middlesbrough edged past Hull City with a 4-3 replay win at the Riverside in the third round, a result that has encouraged Johnson.
"They scrapped through 4-3 against Hull, so if they are conceding goals then that is good for us.
"We'll give them a good game and we will be very positive and try to win the tie."
Middlesbrough edged past Hull City with a 4-3 replay win at the Riverside in the third round, a result that has encouraged Johnson.
"They scrapped through 4-3 against Hull, so if they are conceding goals then that is good for us.
"We'll give them a good game and we will be very positive and try to win the tie."