The 19-year-old Johnson, who has penned a four-year deal, has been first choice in City's midfield under new manager Sven-Goran Eriksson and scored his first goal for the club with the only goal against Derby.
A few days later he was handed his first England Under-21 cap by former City boss Stuart Pearce.
Youngster Logan has signed a new three-year contract.
The versatile 19-year-old product of City's youth academy impressed during the pre-season tour of Sweden.
City's chief executive Alistair Mackintosh said: "In awarding new contracts to Michael and Shaleum we are once again demonstrating Manchester City's commitment to investing in our young, home-grown players.
"With a spine of hugely-talented academy-bred youngsters we have made an excellent start to the season and are delighted to have secured the long-term futures of both players at this football club."