Edelman received the four-game suspension in June for violating the NFL's policy on performance-enhancing substances. His appeal was rejected and he'll miss the first month of the regular season.
The veteran is allowed to participate in training camp but won't be eligible for reinstatement during the regular season until Week 5.
Edelman refused to identify the substance involved in the positive test.
"I've got to follow the protocols a little better and make sure this never happens again," he said, according to the Boston Globe. "I'm accountable for my actions, and ultimately my focus now is getting my knee right and going out and trying to play football at a high level. ...
"It's disappointing with the penalty and the findings, and you know, I'm definitely accountable for that."
Edelman is returning this year from a preseason knee injury that caused him to miss the entire 2017 season. Combined with the suspension, he will have missed 23 consecutive regular-season games when he eligible to return.
"It was a hell of a year to just sit and watch your team go to a Super Bowl and play without you and you're on the couch," Edelman said. "And, you know, it was tough."
The suspension will force him to miss games against the Houston Texans, Jacksonville Jaguars, Detroit Lions and Miami Dolphins. His first game back would be Thursday Night Football on Oct. 4 against the Indianapolis Colts.
"Right now, my focus is tomorrow, and today, and learning from the film, and going and critiquing my cuts and critiquing my football ability right now," he said. "It's been 11 months since I've been able to run, out of surgery, so I'm focused on that. And it's good to be back out here and get to throw the pads on, compete, and go out and earn your teammates' trust, respect. And that's what I look forward to doing."
Edelman and quarterback Tom Brady met with the media Saturday and fielded questions about a connection to Brady's "body coach" and business partner Alex Guerrero. Edelman refused to go into details about Guerrero, who said last month he was not involved in Edelman's positive PED test.
"What's in the past is in the past," Edelman said. "I love Alex. Ultimately, I'm about just going out here and playing football. I'm not here to talk about ... make a headline on something. Just here playing football, buddy."