The cornerback from Texas will receive $8 million guaranteed under the deal that he signed on Thursday.
"From day one I wanted to be out there with the vets, with the rookies and the coaches, everybody," Ross said in front of his dormitory at the University at Albany. "In two weeks we have a preseason game and I didn't want to miss any time."
Corey Webster and veteran Sam Madison are the incumbents at the cornerback spot with R.W. McQuarters returning as the nickel back.
The Giants are hopeful that Ross, who had six interceptions in his final year at Texas, will be able to contribute to a secondary that struggled last season.
"I am not thinking about starting at all," said Ross, the 20th pick overall. "I am just trying to learn the system. R.W. and Sam have been helping me a lot. Once I learn from them and get everything under me, whatever happens, happens."
Ross also may be used as a punt returner. He averaged 11.8 yards in college.
Smith believed his contract was four years in length. Ralph Cindrich, his agent, did not immediately return a telephone call left by The Associated Press, seeking comment on the deal.
With veteran Amani Toomer coming off major knee surgery, Smith will have a chance to play a lot in training camp.
"It's a lot like the first year at college," said Smith, who had 190 career receptions for 22 touchdowns with the Trojans. "It's a bunch of guys who are eager to get on the field. We've been out of football for a few weeks and we're excited. There is always something to prove."