Cottrell, 56, gets a two-year contract to replace George O'Leary, who left the Vikings to become head coach at Central Florida.
"We were excited when his name became available and more
excited that we can add him to our staff," Tice said. "He will
bring a wealth of experience and knowledge. ... He's a very good
developer of young talent."
A veteran of 20 years in the NFL, Cottrell was a man in demand after the Jets dismissed him. He was quickly contacted by Tice, then interviewed over the weekend with San Diego coach Marty Schottenheimer and was being sought by Pittsburgh for an interview. The Vikings were especially aggressive in their courtship.
Sources said Tuesday that Bill Bradley, also dismissed in the Jets' purge of their defensive staff, could join Cottrell in Minnesota. Bradley was the Jets' secondary coach but, if hired, would serve at Minnesota in a different capacity.
The firing of Cottrell came less than a year after he came very close to landing the San Francisco 49ers head coaching job following the firing of Steve Mariucci.
Reports began about mid-season that Jets coach Herm Edwards preferred a coordinator whose philosophies were more in line with his, and who would use a scheme like the "cover two" popularized by the Tampa Bay Bucs. While Edwards was publicly supportive of Cottrell, most team insiders realized a change was coming.
Cottrell was credited with the turnaround of the New York defense in 2002, when the unit began the season slowly, but was among the league's top five during the second half.
That '02 defense, which featured six new starters, finished the season No. 22. The Jets' ranking this year was actually a bit better, 21st overall, and they allowed the eighth-fewest points in the league, 299.
In addition to his three-year Jets tenure, Cottrell's resume includes stints with Kansas City (1981-82), Buffalo (1986-89 and 1995-2000), and Arizona (1990-94).
Len Pasquarelli is a senior writer for ESPN.com. Information from The Associated Press was used in this report.