Smith played for the Giants from 2007 to 2010, totaling 220 receptions for 2,386 yards and 11 touchdowns. Smith made the Pro Bowl in 2009, when he posted a franchise-record 107 receptions for 1,220 yards and seven touchdowns.
Last season, he was limited to nine games due to injuries and finished with 48 receptions for 529 yards and three touchdowns.
Smith sustained a season-ending left knee injury Dec. 13 in the Giants' win over the Vikings at Ford Field in Detroit, and had microfracture surgery eight days later.
Smith visited with the Giants Monday and Tuesday, including an examination of his knee. Giants coach Tom Coughlin said Smith still had "a ways to go" before being healthy enough to 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, 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 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."
Sources with knowledge of Smith's medical review by the Giants and Eagles told ESPN NFL senior analyst Chris Mortensen that doctors realistically believe the wide receiver could return by mid-October if he suffers no setbacks in his rehabilitation.
Under that projected timeline, Smith likely would begin the season on the PUP (physically unable to play) list, meaning he would be required to miss the first six regular-season games. The Eagles have their bye in Week 7.
But a source tells ESPN NFL Insider Adam Schefter that the Eagles expect Smith to contribute early on and not start the season on the PUP list.
Smith had been expected to re-sign with the Giants, but a source told ESPNNewYork.com's Ohm Youngmisuk that the holdup over Smith's signing had to do with his health and the fact that the receiver likely will not be ready for the start of the season.
Apparently the Eagles harbored no such reservations, nabbing Smith away from their NFC East rivals.
Smith enters a crowded 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 in a statement. "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 the past two weeks, following cornerbacks Dominique Rodgers-Cromartie and Nnamdi Asomugha, defensive end Jason Babin, quarterback Vince Young and running back Ronnie Brown.
"Like I've said many times before, (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."
Information from ESPNNewYork.com's Ohm Youngmisuk, ESPN senior NFL analyst Chris Mortensen and The Associated Press was used in this report.