The former Manchester City midfielder completed his move to the Stadium of Light on Friday for a fee understood to be around £10 million, with the Black Cats also capturing Steven Fletcher from Wolves earlier on the same day for a reported figure of £12m.
The Black Cats' manager revealed the winger tried to complete the move in time for their clash with Reading on Saturday, before it was postponed due to a water-logged pitch, but instead indicated he will make his debut in the League Cup second-round clash.
The 60-year-old told reporters: "After playing for England, Adam is a lot fitter than Steven Fletcher.
|BLACK CATS SHOW THEIR TEETH?
|16/1||Sunderland are 16/1 with Bet365 to beat Morecambe 5-0 in the League Cup on Tuesday|
"I think it would be a great opportunity for him. He will be playing."
The manager will be hoping that the duo can add goals to a front-line which managed just 45 last season, although Louis Saha has already been brought in as well with Asamoah Gyan leaving the club for Al Ain.
The former Aston Villa boss is looking forward to seeing his new men in action, while suggesting they have more creative quality in their ranks this term.
"Fletcher gives us a bit of a new dimension," he continued. "I would love to promise that we will score a lot more goals with those two in the team, but I do get the impression we will create more chances.
"Johnson is a very exciting player. He just needs more encouragement to keep going.
"He is the type of player I love - someone who takes opponents on. I used to do it myself - without great success."
|"Fletcher gives us a bit of a new dimension. I do get the impression [that] we will create more chances"
- Martin O'Neill
Although Johnson is in line to play for the Black Cats, O'Neill will most likely use the fixture as an opportunity to rotate his squad, just as many other managers do.
However, the former Aston Villa boss insists he is taking the competition seriously, and hopes his team can put on a show for the home crowd.
"The cup tie is very important for us," he added. "We had a taste for the cup last year and the atmosphere that night against Everton in the replay was extraordinary.
"It showed just what it means to the people here. We would love to do well.
"We have a home tie and really want to make the most of it. We just want to give it a real go and show people what we want to do.
"I have not had the chance to see Morecambe myself, but we have reports and we will look at video coverage of them.
"We want to do really well in the cup competitions."