Between the time of his DUI arrest and his return to the Cardinals, Abraham spent some time in a rehab facility, league sources told ESPN's Adam Schefter.
Abraham, the NFL's active sacks leader, underwent a physical and then spent the afternoon meeting with trainers and Buddy Morris, the team's strength and conditioning coach.
"He's here and ready to roll," Arians said.
There's no doubt in Abraham's mind that he'll be primed for the rest of training camp and is eager to get back on the field again and rejoin his teammates.
"Definitely I'm ready to play and ready to get the pads on, get back in and just being around football team and just being around my teammates, that's probably the biggest thing I missed," Abraham said. "Football gonna come and go but the relationships that you have with the guys are the biggest thing."
Awaiting Abraham will be his old job. Arians said Abraham will be the Cardinals' starting weakside linebacker. He had 11.5 sacks and made his fifth Pro Bowl last season after becoming a starter in Week 4. His ability to play against the run after years of being a situational pass-rusher kept Abraham in the starting lineup in 2013.
This year, Arians already expects much of the same.
"He'll come off the field very seldom," Arians said, "unless he taps out and is tired."
Abraham, who was arrested on June 29 and charged with DUI in suburban Atlanta, spoke to reporters after putting in afternoon work with the team's training staff.
"We know he had to go through what he did to get back to here," Arians said. "We're all behind him. Right now it's just physical and getting in shape and getting ready to go."
Abraham acknowledged that he still needs to lose some weight to get back to game shape.
"I actually gained weight," he said. "Eating a lot of candy. Everybody say that. I look big as hell. I guess (it's) in the eyes of the beholder. I gained a little bit of weight. I couldn't run like I wanted to. Definitely I'm ready to play and ready to get the pads on get back in and just being around football team and just being around my teammates, that's probably the biggest thing I missed."
Arians didn't seem concerned about the 36-year-old getting back into shape after missing Arizona's offseason OTAs and minicamps and the first 19 days of camp, which included 14 practices and a game.
"He showed up last year [on] the first day of training camp and he got himself ready to play," Arians said. "So I have all the confidence in the world he'll get himself ready to play."
Also Thursday, the Cardinals announced the signing of former Green Bay Packers linebacker Desmond Bishop. Arians said Bishop will add to the team's depth at inside linebacker.