The former Middlesbrough winger missed out on a place in Hodgson’s 23-man travelling party for Euro 2012 after starting just 10 games for Manchester City last season.
Johnson completed a £12m switch from the Eastlands outfit to the Black Cats last month, signing a four-year deal at the Stadium of Light.
And Sunderland skipper Cattermole is expecting the England international to have a big impact at the club, with the midfielder confident Johnson will improve further under Martin O’Neill.
“To come back to the north east, he will get a lot of attention around here. Sometimes that’s hard to handle,” said Cattermole.
“But Johnno’s a great lad and he’s shown the desire to come because he wants to play.
“He’s going to further his career, kick on and be a full England international all the time. I’m sure when the next World Cup comes along, he’s going to be in it.”
He added: “Once the club got permission to speak, I gave him a ring and said. ‘You will absolutely love it’.
“It’s a big thing for him. He played in the team that won the Premier League last year. It was a big ask for him to come away from there.
“Johnno is a phenomenal player and to have him here at the age he’s at is brilliant for the club. He’s in the prime of his career and he’s only going to get better.”