Johnstone, who won the last of his four England caps in 2023, made 17 appearances last season but lost his starting place at relegated Wolves in December and has not played since an FA Cup loss to Liverpool in early March.
“I’m buzzing to be here and I’m excited to get going,” said the goalkeeper, who began his career at Manchester United and has had spells at Aston Villa, West Bromwich Albion and Crystal Palace.
“I didn’t need convincing by anyone, but Joe Hart rang me the other day just to reiterate what a place this is, what a great group of lads and how the fans are unbelievable.
“You hear about the size of the club, but just being here for a day, you notice how big the club is. And the pressure to win, which is what I like – pressure to win, pressure to perform and we all want to win trophies.”
Kasper Schmeichel had been first choice at Celtic since the summer of 2024, but played his last game in February and subsequently retired because of a shoulder injury.
Manager Martin O’Neill said Johnstone would be “a very good addition” and that Mheuka has “great quality”.
O’Neill also said new left-back Emenalo “has many attributes which I think can benefit us”, adding he is “very quick on the ball and, while he can defend, he certainly gets up the pitch into attacking positions too.”