The 26-year-old Smith had 220 catches for 2,386 yards and 11 touchdowns in four seasons with the Giants. In his 2009 Pro Bowl season, he caught a franchise-record 107 passes for 1,220 yards and seven touchdowns.
Smith sustained a season-ending left knee injury in the Giants' win over the Vikings at Ford Field in Detroit on Dec. 13 and had microfracture surgery eight days later.
He said Wednesday night he believes he'll be able to play soon. "I think I'm pretty close," Smith said. "I think I can realistically be out there (the first month). It could be week one. You never know."
Giants coach Tom Coughlin told reporters Wednesday after meeting with Smith that he believed Smith faced a "long haul" before he could play again.
"I would disagree with that," Smith said. "I feel good. I've been running, cutting, doing different things. I haven't had any setbacks."
Smith said he was examined by doctors from both the Giants and Eagles and said both gave him a positive report.
Asked why Coughlin might have indicated that Smith faced a longer rehab than Smith's doctors expressed to him, Smith said, "Maybe Coughlin had a plan up his sleeve when he said that. We'll see what happens when I get out on the field."
Smith said he believes the real reason the Giants didn't want him was financial.
"Yeah, shoot," he said.
Smith said he couldn't speculate exactly when he'll be able to return to practice.
"I'm not sure," he said. "If it was up to me, I would say I could go practice tomorrow, but I want to be extra careful and don't want to rush it and have any setbacks. Hopefully, I'll be able to get out there really soon."
Smith enters a crowded wide receiving field with the Eagles, who also have two-time Pro Bowl pick DeSean Jackson; Jeremy Maclin, who caught 70 passes last year but hasn't practiced yet this training camp because of an undisclosed illness; Jason Avant, who caught 50 passes last year; and second-year pro Riley Cooper.
"We feel very good about our current group of receivers and Steve adds another dimension to that position," Eagles coach Andy Reid said. "He's played very well against us in the past few years and we're happy to have him on board."
Although Smith was almost exclusively an inside slot receiver in his four years with the Giants, Smith said he's equally comfortable in any role.
"I feel great inside, outside," he said. "The Giants used me mainly inside, but I feel like I can do both."
Smith is the sixth Pro Bowl player to join the Eagles in last two weeks, following cornerbacks Dominique Rodgers-Cromartie and Nnamdi Asomugha, defensive end Jason Babin, quarterback Vince Young and running back Ronnie Brown.
"(General Manager) Howie Roseman and I are always keeping our eyes open for good football players and players that we think can help our football team win," Reid said. "And Steve Smith certainly fits that category. He's a Pro Bowl-quality receiver that we will work into our offense as soon as he is ready to go."