Ben Foster, 27, has joined McLeish's Birmingham City in a £6million, three-year deal from Manchester United and will succeed Hart, who ended an outstanding loan spell to return to Manchester City.
Hart is now with England preparing for the World Cup, while Foster's career has nose-dived.
Foster started the season as United's No1 but has recently found himself out of favour with both club and country.
"I believe Foster is of the same standard as Hart, " said McLeish.
"His situation is similar to Hart's in that he found himself twiddling his thumbs. We feel Foster is a very capable player who can make a name for himself. "
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