Wright knows Derbyshire well, having played for the club during his career as a New Zealand batsman.
Last season saw Wright guide Derbyshire to their first Twenty20 quarter-final in more than a decade before they were undone Pakistan star Shahid Afridi's blistering 42-ball century for Hampshire.
Wright will be back working alongside former Derbyshire and England seamer Dominic Cork.
"We saw great progress in the shortest format in 2017, securing a home quarter-final for the first time and playing a positive brand of cricket throughout the competition," said Derbyshire cricket advisor Kim Barnett.
"Our ultimate aim is to reach Finals Day and bring silverware to Derbyshire.
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