The 44-year-old, who has led both South Africa and New Zealand's A teams, replaces Brian Rose who stepped down from the role after Somerset again narrowly failed to win a trophy last season.
Nosworthy has never previously coached in England and is due to take up the post in February and said: "I am absolutely delighted to be coming to Somerset along with my family. The club has a proud tradition, is currently in great shape, and is clearly an exciting place to be."
Nosworthy quit his most recent appointment at the Highveld Lions in June and had been short-listed for the New Zealand job.
The chairman of Somerset's cricket committee, Vic Marks, said Nosworthy's appointment had been a unanimous decision.
"We interviewed candidates from all over the world, those with exceptional playing backgrounds and international coaching experience, but there was no doubt that Dave Nosworthy was the outstanding candidate and the panel were unanimous in their decision," he said.
"The director of cricket's role is a very broad one requiring excellent cricketing knowledge and experience, combined with strong leadership and communication skills - Dave demonstrated all of these during the extensive selection process and he is undoubtedly the right man to take the club forward."
Nosworthy's appointment came on the same day all-rounder Peter Trego signed a new three-year deal.
The 31-year-old enjoyed his most successful season to date last term as his 50 County Championship wickets and 600 runs, combined with some fine one-day performances, earned him the 2012 Most Valuable Player award.
"Signing this new contract means that I will be playing for Somerset into my mid-30s, which is a huge personal achievement," he said. "Not many players have a career that length so I am very fortunate to get this opportunity with the club that I love playing for."
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