The Cowboys' all-time sacks leader, is one of the biggest names to be made a free agent as National Football League clubs pared down costs to gain room under the league's salary cap.
"A decision like this, involving a man who is a cornerstone player in the history of your franchise, is extremely difficult," Jerry Jones, owner and general manager of the Cowboys, said in a statement.
The 31-year-old Ware, drafted 11th overall by Dallas in 2005 and fourth in career sacks with 117 among active players, twice led the NFL in sacks and four times has been named to the first-team All Pro list.
In an injury-hit 2013 campaign, Ware registered six sacks to snap a streak of seven successive seasons with double-digits in sacks including 20 in 2008 and 19.5 in 2011.
Ware, who turns 32 in July, was set to count $16 million against the cap with a $12.25 million base salary, ESPN reported.
(Reporting by Larry Fine in New York; Editing by Frank Pingue)