The former Newcastle boss, 52, is understood to have beaten off competition from Roberto Di Matteo in the battle to take charge of the relegated Carling Cup winners.
"Following productive talks with the former Newcastle boss, acting chairman Peter Pannu felt that Hughton was the perfect candidate to take charge at St Andrew's and he is now looking forward to sharing the new man's ambition," the club said in a statement.
"Terms were agreed today and Hughton takes charge with immediate effect."
Hughton has been out of football since parting company with Newcastle after a 3-1 defeat at West Brom in early December despite the Magpies being in mid-table in the Premier League in their first year back in the top flight following promotion.
Yeung is looking for Blues to regain their Premier League status at the first attempt as was made clear to McLeish in a statement issued at the end of the season.
Hughton has plenty of experience at Championship level and guided Newcastle to promotion 13 months ago as champions.
London-born but a former Ireland international defender, he was previously a member of the coaching staff at Tottenham.
Because of their cup win, Birmingham will have the unusual distinction of representing England’s second division in the Europa League.