Witherspoon will receive $5 million in the first year of the contract, a league source told ESPN NFL Insider Adam Schefter.
"Knowing the organization and knowing coach [Jeff] Fisher and [linebackers] coach [Dave] McGinnis and kind of getting a better idea of what's going on, all that kind of came into play," Witherspoon said Wednesday. "I'm going to do my best to make sure everybody knows what I've brought to the table here."
Witherspoon was released by the Eagles last week. He was traded to Philly in exchange for rookie receiver Brandon Gibson just prior to the trade deadline.
He started at both middle and weakside linebacker for the Eagles.
"My release in Philly was kind of a surprise to everyone. That just kind of came about, but the opportunity to come here arrived, and I said I definitely have to take a look at this," Witherspoon said.
For the 2009 season, spanning his time with both teams, he racked up 91 tackles and a sack and also returned his only interception for a touchdown.
Titans general manager Mike Reinfeldt says Witherspoon will likely play outside linebacker.
"In eight years, the best thing about it, my only issue ever is that I had one minor scoping. In eight years, I've only missed four games," Witherspoon said.
"I feel like I've got a lot of good years left in me. If you had asked me eight years ago how long I thought I would play, I wouldn't know. But if you ask me the same question today, I feel like I've got plenty more left in the tank. I don't think people should be worried about me. If I get the choice, there's a good possibility I'd like to finish my career here," he said.
Information from The Associated Press was used in this report.