The 56-year-old ex-Derbyshire skipper leaves his post as club president to take the newly created job.
Graeme Welch left as elite performance director in June, having been appointed following a management revamp in 2014.
"We have not achieved enough success in recent years. We're determined to change this," said Barnett.
"With a strong captain and players technically sound and tactically clued up, we will be in a great position for next season."
Derbyshire finished bottom of Division Two, having failed to win a County Championship match in 2016.
A review of the "cricket pathway to the first XI" was undertaken, with a new coaching structure put in place alongside a "targeted" recruitment drive for experience senior players, which will be funded by savings made by revamping the coaching team.
Barnett will head a smaller backroom staff "streamlined" and aided by player-coaches, who will work "occasionally" with specialised "world class" coaches and cricketers.
The new structure sees the post of first XI support coach and Twenty20 specialist coach created - neither of which have been filled yet.
"The Elite Performance model regrettably has not produced the results that we have been hoping for," Derbyshire chairman Chris Grant told the club website.
"We have been spending over 20% of our overall cricket budget on coaching and this new model will achieve a better balance between our coaching and playing budget."

The 56ft (17.1m) converted trawler was 6 miles (10 km) west of South Stack when the crew radioed coastguards at 07:00 BST.
Holyhead coastguards said a pump on board the boat was unable to cope with the water coming in.
The RNLI lifeboat crew placed a pump and towed the vessel to Holyhead.

TrueTube, an educational platform, has been named a contender for three awards in total, including best drama and secondary learning.
Horrible Histories also earned three nominations, all for its special episode celebrating the 400th anniversary of Shakespeare's death.
The awards will be held at the Roundhouse in London on 20 November.
TrueTube's success "demonstrates the shift in how young audiences are consuming media", Bafta said.
The website's drama nomination is for Refugee, a 12-minute film following a British girl and her family who have fled their home, while Katie, about a gay, Catholic nurse in a children's ward, is up for the learning award.
TrueTube senior education producer Bob Ayres said: "We are over the moon. We are a small charity-funded online channel and to be nominated alongside such giants feels like an attack of vertigo.
"We are very, very proud the films we make for young people and schools have been given such recognition, and extremely pleased they will now reach a wider audience."
The Shakespeare special from the gruesomely entertaining Horrible Histories is up for the comedy and writing trophies and actor Tom Stourton will compete for the best performer honour for playing the role of the Bard.
Elsewhere, a number of programmes received two nominations. Cartoon Network's The Amazing World of Gumball is up for the animation and writer awards.
CBBC's Hetty Feather and The Dog Ate my Homework are among the other double nominees.
The annual Bafta Children's Awards also recognise movies which have been on general release in UK cinemas.  This year, the academy has chosen Zootropolis, The Good Dinosaur, The Jungle Book and Star Wars: The Force Awakens for its feature film award.
Star Wars is also in the running for two other awards - best game for Lego Star Wars: The Force Awakens and the adapted interactive prize for Star Wars Arcade.
The full list of categories and nominees can be found on the Bafta website, with voting closing on 18 November.
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Former England batsman Kim Barnett has been named Derbyshire director of cricket in the latest coaching restructure at the Division Two club.
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Three people have been rescued from a boat which had started to take on water off the Anglesey coast on Friday.
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The Bafta Children's Awards have for the first time nominated an online-only service for channel of the year.