The 43-year-old will be number two to new Town boss Yates, coincidentally one of the men he beat to the Newport job last season.
Yates told the club website: “I spoke to three or four candidates but within half an hour of talking to Jimmy I knew he was the right person for the club.
“He’s got a lot of experience of League Two and he’s a very good coach and a bubbly character who will be great around the training ground and the club.
“I’m delighted he’s agreed to join us and I look forward to working with him and helping to take the club forward.”
Dack played for Crawley during two spells in the mid-1990s, making over 100 appearances.