The former Manchester City academy coach leaves the staff at Leicester City to take the manager's job at Cardiff.
Barry-Murphy has penned a three-year deal until the summer of 2028.
Current Manchester City academy coach Lee Riley has been named Barry-Murphy's assistant, having previously worked with him at Rochdale.
Barry-Murphy takes charge after the dismissal of Omer Riza last season.
Tan welcomes Barry-Murphy arrival
Bluebirds owner Vincent Tan said: "Throughout the interview process, Brian showed a huge passion for our club because he believes in what we're trying to do.
"He knows this level having played and managed at this standard before, where he was noted for his style of play.
"Since then, he has only gone from strength-to-strength as a leader.
"He's got a proven track record in youth development having coached some of the brightest young prospects in the UK, many of whom are now playing at the very top of the game.
"He brings enthusiasm, vibrancy and an exciting outlook on what today's football is, while looking to play an attacking style that our fans are sure to enjoy.
"It's a combination of all of Brian's great talents that make him the right man to take us forward into this next chapter."