The Wings landed the 38-year-old for a relatively low price, giving up only a third-round pick in 2016 in the deal. The pick will become a second-round pick if Detroit reaches the Stanley Cup Final.
"The growth of our team and the growth of our younger players, I guess, sent a message to me that we've got a good team,'' Red Wings GM Ken Holland said. The team also acquired Erik Cole from Dallas on Sunday.
Detroit had earlier expressed interest in Toronto Maple Leafs captain Dion Phaneuf, but a source told ESPN.com's Craig Custance that the discussions never became serious because of philosophical differences between the two sides about the structure of the potential deal.
Zidlicky had a full no-trade clause in his contract with the Devils that he was willing to waive in accepting a deal to the Wings.
The Devils will retain $1 million of Zidlicky's salary, a source told ESPN.com.
ESPN.com's Pierre LeBrun and the Associated Press contributed to this report.