Cardiff had been relegated to League One for the first time in two decades when Barry-Murphy was appointed 13 months ago.
The former Rochdale boss won 27 of his 46 league games, a win rate of 58.7%, during his first season at the Cardiff City Stadium.
With 91 points on the board, they finished second behind Lincoln City, but were the division’s top scorers with 90 goals, one more than the champions.
Barry-Murphy, who previously helped develop talents including Chelsea’s Cole Palmer, has been praised for bedding in youngsters at Cardiff last season.
Defenders Dylan Lawlor and Ronan Kpakio, midfielder Joel Colwill and winger Isaak Davies all made their Wales debuts after working with the Irishman.
“It’s an amazing honour for me, and I’m really grateful to everybody involved,” Barry-Murphy told Cardiff’s club website.
“When I first came here, I had an idea of how big the club was, but over the course of the last 12 months I think I’ve probably seen it in all its splendour, so I’m really pleased.
“The energy that we’ve had from the supporters from the very first day has propelled us forward, at a speed that may have not seemed possible.
“Like anything, once you get things going, moving forward with positivity and with a real togetherness, great things can be achieved.”
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