Wright turned down the chance to follow Steve Lomas to Millwall to take the reins at McDiarmid Park and he will start his tenure with a Europa League qualifier on 18 July.
The 49-year-old, who will be assisted by Callum Davidson, said: "When I finished my playing career in England I made the decision to go back to league football in Northern Ireland to learn my trade, so to be standing here as manager of an SPL club 12 years down the line makes this a very proud moment.
"I'm excited about the challenge ahead and I look at my experience in the game and feel that the fact that I've worked at all levels of the game might be important for this club.
"I've been a youth development officer with the IFA, I've managed part-time clubs, I've worked at Championship level in England at Norwich, I've worked at international level, I've had 18 months in the SPL and I've worked under strict financial budgets.
"Since coming to Saints in November 2011 I've improved the contacts I have up here and combined with the people I already knew I believe I have the sort of contact list the chairman is looking for.
"I've learned a great deal since I came to Perth and improved my knowledge of the game so I think I'm well prepared for the job ahead."