The Bears cut ties with Peppers, who has 118 1/2 sacks in 12 seasons, as part of a series of moves aimed at improving their defence, including a five-year contract with former Raiders end Lamarr Houston.
The Cowboys let Ware and his 117 sacks go.
"A decision like this, involving a man who is a cornerstone player in the history of your franchise, is extremely difficult," Dallas owner Jerry Jones said. "We were also in very strong agreement that playing for the Dallas Cowboys would be one of the options we would both be exploring."
With the cap rising $10 million to a record $133 million, a crop of players quickly found new homes as soon as the market officially opened Tuesday afternoon — and safeties and offensive linemen were popular commodities.
About 5 1/2 hours after free agency began, one of the top players available, three-time Pro Bowl safety Jairus Byrd, agreed to terms with the Saints, part of a merry-go-round of moves at his position. Other safeties swapping clubs: Michael Jenkins, from Saints to Eagles; Donte Whitner from 49ers to Browns; Antoine Bethea from Colts to 49ers; T.J. Ward from Browns to Broncos; Mike Mitchell from Panthers to Steelers; Ryan Mundy from Giants to Bears.
In addition to jettisoning Peppers and adding Houston and Mundy, Chicago agreed to one-year deals with linebackers Jordan Senn and D.J. Williams.
Two of the most sought-after cornerbacks also were on the move. Alterraun Verner, who had five interceptions for Tennessee last season, agreed to a four-year contract with Tampa Bay and Aqib Talib left New England for a six-year deal with Denver.
Verner, 25, could wind up being a replacement for Darrelle Revis, who might be traded or cut to create more salary-cap room for the Buccaneers.
Deals for offensive linemen were highlighted by Pro Bowl left tackle Branden Albert's five-year contract with the Dolphins. Albert left Kansas City to take over the position played at the start of last season by Jonathan Martin, whose exit from Miami in October led to an NFL inquiry into bullying on the team.
Late Tuesday, Martin was traded by the Dolphins to the 49ers.
Left tackle Jared Veldheer and the Cardinals agreed to a five-year contract worth up to $35 million. Veldheer left the Raiders, who replaced him by giving former Rams lineman Rodger Saffold a five-year deal. Another left tackle, Eugene Monroe, agreed to a five-year contract to stay with the Ravens.
Former Jets right tackle Austin Howard agreed to a five-year, $30 million contract, with $15 million guaranteed after starting every game the last two seasons in New York.
AP Sports Writers Bob Baum, Tim Booth, Schuyler Dixon, Josh Dubow, Larry Lage, Mark Long, Michael Marot, Brett Martel, Janie McCauley, Paul Newberry, Teresa M. Walker, Dennis Waszak Jr., John Wawrow, Joseph White and Steven Wine contributed to this report.
Follow Howard Fendrich on Twitter at http://twitter.com/HowardFendrich
AP NFL website: www.pro32.ap.org