Team officials confirmed a deal was done but would not disclose financial details.
CBS Sports reports the deal is a two-year, $21 million pact, but the contract reportedly could be worth a maximum of $40 million over four years.
NFL Network reported the agreement includes $13 million of guaranteed money this year and $8 million for injury only in 2015.
The agreement was hammered out before a 4 p.m. ET Tuesday deadline for franchise players to sign a long-term contract. Graham otherwise would have been eligible for $7.035 million this year as a franchised player.
Graham, who caught 86 passes for 1,215 yards and 16 touchdowns, had fought for compensation equal to a wide receiver, which is $12.312 million for the franchise year.
Orton, 31, has been considering retirement and skipped the team's entire offseason program. His release adds $1.1275 million in dead money to the Cowboys' salary cap this season and $2.255 million in dead money in 2015, according to the report.
However, it does clear his $3.25 million salary against this year's salary cap.
While Orton has not made any public comments this offseason, if he retired under contract he would be required to repay $3 million from his signing bonus.
The Cowboys have been bracing for Orton's departure, adding veteran backups Brandon Weeden and Caleb Hanie over the offseason.
Former Minnesota Vikings punter Chris Kluwe plans to sue the franchise for discrimination unless the team releases the findings of its investigation into the player's allegation that he was subjected to harassment and hostility for speaking out in favor of gay marriage.
Kluwe said the team is not living up to a promise to release those findings, but the investigators denied that claim through a press release. Kluwe said Tuesday he will file a lawsuit for religious discrimination, sexual orientation discrimination, defamation and tortuous interference.
The independent investigators said a meeting is scheduled for Thursday.
Troubled former Detroit Lions receiver Titus Young entered a not guilty plea Monday on one felony count and four misdemeanor counts in a Los Angeles County court.
Young was arrested July 9 in Los Angeles and was charged with one count of battery with serious bodily injury and four counts of battery on school, park or hospital property. The charges stem from five different individuals in a two-month period at a medical facility, TMZ reported.
A preliminary hearing is scheduled for July 24 in Compton (Calif.) Municipal Court, according to the Los Angeles County District Attorney's office. Young's bail was set at $105,000.
Since the 24-year-old Young was waived by the Lions in 2013, he has been involved in a series of run-ins with police.
The Washington Redskins signed free agent fullback Stephen Campbell to an undisclosed contract on Tuesday.
The 23-year-old Campbell, an undrafted free agent from West Virginia Wesleyan, was waived by the Indianapolis Colts on May 12. He had signed with the Colts less than a month earlier.
(Editing by Larry Fine)