The deal is for five years and $11.8 million, with $8.3 million guaranteed, according to a source. The wide receiver received $2.5 million to sign and will earn a base salary of $320,000 this year. He also has bonuses tied in to playing time.
Eugene Parker, Bryant's agent, said some of the language of the contract is still being worked out.
Bryant, the 24th pick of the draft, is expected to report on time for Cowboys training camp on Saturday in San Antonio.
"This was very important to me to be able to get this done in time for the first practice," Bryant said in a statement released by the team. "I want to help this team. I want to compete. I can't wait to start playing football again."
"It was important to get Dez in on time," Cowboys vice president Stephen Jones said. "We think he can be helpful to us. He knows we have a good football team and we're counting on him to be a big part of it."
The Bryant deal is a relief for the Cowboys because there was speculation he would not make it to camp on time. Parker had worked deals with previous Cowboys first-round selections Mike Jenkins and Felix Jones, who both reported late.
Cowboys owner Jerry Jones was assured by Parker that if he drafted Bryant, he would avoid a long, drawn-out contract process.
"It helped to have a sense of urgency because it made the deal get done," Parker said. "Jerry and Stephen and I have a relationship of trust in doing deals and we give each other the benefit of doubt."
Bryant played only three games for Oklahoma State last season, then was dogged by all sorts of questions about his integrity, starting with an NCAA suspension for lying to investigators about a meeting with former Cowboys star Deion Sanders.
There was talk that Bryant skipped meetings and classes and was late to games. There were concerns about his mother's private life, enough that Miami Dolphins general manager Jeff Ireland asked if she ever was a prostitute. After Bryant skipped the NFL combine and held his own pro day, there were whispers that he forgot to bring the right cleats.
But the Cowboys did their homework and wanted Bryant so badly that when they saw him slipping in the draft, they moved up three spots to No. 24 and nabbed him. Jerry Jones gave Bryant No. 88, the jersey worn by Hall of Famer Michael Irvin and, a generation earlier, by Drew Pearson.
Irvin was Troy Aikman's favorite target, and Pearson was Roger Staubach's favorite target. With this deal done, it won't be long before Tony Romo starts his relationship with Bryant, perhaps adding the duo to that list.
"It was really important that we get him working and in the groove with Tony and our offense, and I think he understood that," Stephen Jones said.
Romo liked what he saw from Bryant over the summer -- and from what the kid did in college.
Bryant was an All-American in 2008 at Oklahoma State when he had 87 receptions for 1,480 yards and 19 touchdowns. In 27 games at Oklahoma State, Bryant had 147 catches for 2,425 yards (16.5 yards per catch) and 29 touchdowns. He also returned 22 punts for a 19.6-yard average and three TDs.
The only draft pick yet to agree with the Cowboys is second-rounder Sean Lee, a linebacker from Penn State. The Cowboys expect to finalize his deal Friday.
"I'll be surprised if [Lee] misses anything," Stephen Jones said.
Calvin Watkins covers the Cowboys for ESPNDallas.com. You can follow him on Twitter or leave a question for his weekly mailbag. Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.