The 48 year-old, who had previously worked with the Buckinghamshire club's strikers last term, has been offered a part-time role and will continue his work as a radio pundit at weekends.
Wright told the club's official website: "I am thankful to Karl [Robinson, manager] for allowing me the chance to start my coaching career and I am already excited about the new season.
“I have spent the last year around MK Dons Football Club and I am delighted to now be part of the set-up.
"The group of players we have at MK Dons are an extremely talented bunch and I am looking forward to working with them on a daily basis."
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The 31-year-old hopes that Wright can make a difference next season after his team just missed out on promotion this year, losing to Huddersfield 3-2 on aggregate in the play-off semi-final.
Robinson enthused: "I believe I've picked the best to help our promotion ambitions next season.
"Ian Wright hasn't got his qualifications yet but he is working towards them and he will provide invaluable experience, knowledge and inspiration to our players.
"For a while Ian will work with the team through the week, he can't be with us at weekends because of other contractual commitments, but he will be involved in all our midweek games."