Rose has stepped up from his previous role as secretary and vice-chairman to succeed the long-serving Myer.
The pair have effectively swapped roles, with Myer joining Gary Louis as vice-chairmen in the summer shake-up.
Rose said: "There has been a change. But Brian, after four stints and 48 years on the committee, will still have a major role to play moving forward. I've learned a lot from him. He has taken the league into the modern era and embraced change.
"He simply wanted to hand the role onto someone younger. This is the strongest committee that I've know in last 20 years."
Russell Bernstein has been named as the new secretary while Mark Mann gives the players a voice as a representative on the committee in a newly-created position.
Rose commented: "It's important that there is a link between the committee and players. Having an understanding of league decisions and also having an input is important for us moving forward."
Meanwhile, the MJSL will feature two new teams next season. South Manchester Sports 1st are back following a spell in the Accountants League and the Cheshman League. They will be joined by the newly-formed Sedgley Park Celtic.