It ends Cardiff's prolonged search for a new manager having sacked Omer Riza just weeks before their relegation from the Championship was confirmed last month.
Charlton Athletic's Nathan Jones and Wales captain Aaron Ramsey, who had taken temporary charge after Riza's departure, had been targeted by Cardiff during the process.
But Barry-Murphy emerged as the frontrunner for the role after advanced talks last week and will now be given the task of preparing the team for the club's first season back in the third tier since 2003.
He leaves his role at the King Power Stadium having been appointed to Ruud van Nistelrooy's backroom in December, Cardiff paying compensation for his services.
Prior his time at Leicester, Barry-Murphy had been under-23s boss at the Etihad for three years, helping the development of the likes of Cole Palmer.
His work with young players was of appeal to the Cardiff hierarchy who are keen to utilise several promising academy graduates as they look to return to the Championship.
A former midfielder with Preston North End and Sheffield Wednesday, it will be Barry-Murphy's first frontline manager role since a two-year spell at Rochdale where he also won praise for the side's style of play and use of local talent.
In a statement, 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."