The team made the official announcement Monday.
Ireland agreed to part ways with the Dolphins on Jan. 7, ending his six-year stint with Miami.
Miami reached the playoffs only once in Ireland's six seasons with the team. The Dolphins' 2013 season was marred by the bullying scandal involving offensive linemen Jonathan Martin and Richie Incognito.
The Dolphins also received mixed results from their high draft picks during Ireland's tenure.
The team selected four-time Pro Bowl offensive tackle Jake Long with the first overall pick in 2008, less than four months after Ireland was hired.
Miami's other first-round picks under Ireland were cornerback Vontae Davis (2009), defensive lineman Jared Odrick (2010), Pro Bowl offensive lineman Mike Pouncey (2011), current starting quarterback Ryan Tannehill (2012) and pass-rusher Dion Jordan, the third overall pick last year.
The reigning Super Bowl champion Seahawks own the 32nd overall pick in the draft, which begins May 8.
General manager John Schneider and Ireland both worked for the Kansas City Chiefs from 1997 to 1999.
ESPN Senior NFL Insider Chris Mortensen and ESPN.com Dolphins reporter James Walker contributed to this report.