Bryant, 29, joined the franchise as the No. 24 overall pick in the 2010 NFL Draft. He was a three-time Pro Bowler and was an All-Pro selection in 2014.
The eight-year veteran had a career-worst 12.1 yards per catch last season, totaling 838 yards and six scores on 69 receptions.
Bryant signed a five-year, $70 million contract with the team in 2015.
"As an organization we hold Dez Bryant in the highest regard, and we are grateful for his passion, spirit and contributions to this team for the past eight years," Cowboys owner Jerry Jones said in a statement. "He will always be a valued member of our family."
"Dez and I share a personal and professional relationship that is very strong, and he is one of just a handful of players with whom I have become that close to over the past 30 years."
"This was not an easy decision. It was made based upon doing what we believe is in the best interest of the Dallas Cowboys."
"We arrived at this crossroad collectively with input from several voices within the organization. Ultimately we determined it was time to go in a new direction."
Bryant tweeted several times before and after he met Cowboys brass at the Ford Center at The Star, the team's headquarters in Frisco, Texas.
Cowboy nation I need you to know this wasn’t my decision.. I will always love y’all... forever Dallas in my heart— Dez Bryant (@DezBryant) April 13, 2018
"Let's start the process," he tweeted. "#Unbothered. #ThrowUpTheX."
"Cowboy Nation, I need you to know this wasn't my decision ... I will always love y'all ... forever Dallas in my heart," he added.
If I didn’t have my edge I got it now... I’m sorry they got to feel me it’s personal... it’s very personal— Dez Bryant (@DezBryant) April 13, 2018
"If I didn't have my edge I got it now ... I'm sorry they got to feel me it's personal ... it's very personal," Bryant wrote.
Bryant should have plenty of suitors on the open market, despite his slippage in production last season. He was set to make $12.5 million this season with the Cowboys.