Dee will play in the Ladbrokes Championship next season.
Relegated Dundee have announced the departures of 14 players including recent captain Martin Woods.
The midfielder joins goalkeeper Elliott Parish and defender Genseric Kusunga in leaving following the end of their contracts.
Faissal El Bakhtaoui and James Vincent will not return to the club after spending the season on loan with Dunfermline.
Loan signings Seny Dieng, Ryan McGowan, James Horsfield, John O’Sullivan, Scott Wright, Ethan Robson, Andy Dales and Andreas Hadenius have also left.
Darren O’Dea, who announced he was retiring from playing last week, is also departing.
A Dundee statement read: “The club would like to thank each of these players for their efforts and wish them all the best for the future.”
Goalkeeper Jack Hamilton, full-back Nathan Ralph, strikers Kenny Miller, Andrew Nelson and Craig Curran plus centre-backs Josh Meekings and Andrew Davies remain under contract.
The contracts of young players Cammy Kerr and Jesse Curran are both due to expire at the end of the month.
Midfielder Paul McGowan’s deal is also set to end but there is a 12-month option to extend.
Retiring Darren O’Dea sent off in final match