Rosenior succeeded Enzo Maresca last week after the latter was sacked by Chelsea on New Year's Day.
From what he's seen of the former Strasbourg coach, Johnson believes Rosenior can prove a positive appointment.
He told Tribalfootball.com: “Liam Rosenior’s first game in charge (FA Cup win at Charlton) of Chelsea went about as well as it could have. He got a great result, and Chelsea put in a good team performance. I have seen clips of him, and he looks like he’s settling in.
"Most importantly, he looks like he’s up for the fight, which you have to be as Chelsea manager. Time will tell how the team performs, but I’m optimistic about Rosenior."
Johnson continued: "I definitely have sympathy for Maresca. I always feel for managers who lose their jobs, especially Maresca, who at times had Chelsea playing the best football they have played in three or four years.
"I think what lost him his job was the lack of consistency in Chelsea’s performances. They want to win titles, and you can’t afford to drop points at home to the weaker teams in the league if you want to challenge Arsenal and Man City.”
Meanwhile, on how Chelsea's players can handle so much uncertainty inside the club, Johnson concedes it can be difficult.
He stated: “It is difficult to concentrate and perform as a player when constant changes are going on at the club. In recent times, if it’s not the manager, it’s the staff or the players. There is so much going on at Chelsea. However, as a player, you just do your best to ignore it and do your job.
“You must adapt, and these Chelsea players have to adapt again. However, what the club is looking for is consistency in performances, which the players didn’t find under Enzo Maresca this season.
"Hopefully, they all take on Liam’s ideas and philosophies quickly and pick up consistent results. Changes happen constantly, and that’s the life of a footballer, it’s difficult, but the sooner you adapt, the easier things seem.”
Glen Johnson was speaking to Tribalfootball on behalf of WDW Bingo