"Johnny knows there are areas in which he needs to improve in order to be a better family member, friend and teammate, and he thought the offseason was the right time to take this step," Beckworth said.
"On behalf of Johnny and his family, we're asking for privacy until he rejoins the team in Cleveland."
Manziel is expected to be in rehab at least a few weeks, but the amount of time depends largely on what doctors recommend, according to a source close to Manziel.
A source said the Browns are tentatively expecting Manziel to participate in training camp but are not placing any timetables on other offseason activities as he works through the treatment process.
The quarterback is voluntarily entering treatment as a direct result of his lifestyle away from the field, and he informed people in his circle last week that he wants to "figure out his value system," a source said.
A source told ESPN's Darren Rovell that a casino in Las Vegas offered Manziel six figures to host a Super Bowl party, but he declined.
Browns general manager Ray Farmer said in a statement that the team supports Manziel's decision.
"We respect Johnny's initiative in this decision and will fully support him throughout this process. Our players' health and well-being will always be of the utmost importance to the Cleveland Browns," Farmer said.
"We continually strive to create a supportive environment and provide the appropriate resources, with our foremost focus being on the individual and not just the football player. Johnny's privacy will be respected by us during this very important period and we hope that others will do the same."
Manziel, who has an endorsement deal with Nike, also received words of support from the shoe and apparel company.
Browns receiver Andrew Hawkins tweeted his support for his quarterback on Monday.
Much love and support to my brother Johnny. Proud of him, big step. Football is secondary. God Bless!— Andrew Hawkins (@Hawk) February 2, 2015
Folks criticize Manziel for trying to get help and laugh at overweight people in the gym...they are trying to fix a problem support them smh— Torrey Smith (@TorreySmithWR) February 2, 2015
"I haven't talked to him. I found out about the information when you guys found out about it," James said Monday night. "If it's a guy that's seeking help, then as a friend I support him and want him to get better. And his friends and family, we all believe in him and we think this is a good step if that's the route he's going to take."
Interviews by ESPN.com with nearly 20 Browns sources, both on the record and on condition of anonymity, along with several NFL personnel sources for a Jan. 23 story revealed that Manziel's problems ran deep in his rookie season.
Sources talked of a yearlong pattern that showed a lack of commitment and preparation, a failure to be ready when given a chance in his first start against Cincinnati and a continued dedication to nightlife, which affected his preparation and work while he was in the team facility.
On Dec. 23, a Tuesday in the final week of the season, Manziel stood in front of about 20 media members and outlined his plan to become the Browns' answer at quarterback. He wanted to be "the guy" for Cleveland, he said, and would do so by taking his job more seriously in the offseason. He was more animated than he'd been all year, eager to declare his intentions.
But four days later, the day before the Browns' season finale on Dec. 28, stories in the Browns' facility began to circulate. That morning the Browns were packing up to head to Baltimore, but Manziel was not present for the walk-through. Team security drove to Manziel's downtown home to check on him.
Two team sources said security found a player who they felt clearly had partied hard the night before. One source used the words "drunk off his a--."
The official word was that Manziel was "late," but players said they didn't see Manziel until the Browns' chartered airplane prepared to take off in the afternoon and that he was not present all morning. The team fined Manziel for missing treatment on his injured hamstring, then had him sit in the locker room during the season finale that Sunday against the Ravens.
"Johnny's his own worst enemy," one source said.
Manziel had another news conference the next day, saying many of the same things from six days earlier: Actions must support words. He was featured in Instagram photos that night on Miami Beach, a few days later at a club in Houston and a few days after that on a mountain in Aspen, Colorado.
"I brought this on myself," Manziel said the day after the season ended. "I brought these cameras and all these people that are in this locker room right now, and I don't think it's fair to myself, I don't think it's fair to anybody in this locker room the distractions I've brought at points in time."
Manziel, selected by the Browns with the 22nd overall pick in the 2014 draft, completed 18 of 35 passes for 175 yards in seven quarters of NFL play before injuring his hamstring in Week 16.
ESPN.com's Pat McManamon and Dave McMenamin contributed to this report.