General manager Mike Reinfeldt walked out as coach Jeff Fisher talked to reporters and gave him the news that the Griffin had agreed to terms.
"I wanted to give you something to talk about," Reinfeldt said.
Fisher already said he wasn't worried about getting Griffin signed and that he thought they were close to filling out the paperwork. Fisher said they will start the former Texas safety at cornerback to see if he can help fill the void left by the season-long suspension of Adam "Pacman" Jones.
Griffin had eight interceptions at Texas where he started at free safety last season alongside his twin brother, Marcus. He also blocked eight kicks in his career, including six punts.
The safety was the last to reach terms as the Titans wrapped up the final two of their 10 draft picks Friday. Second-round pick Chris Henry agreed to a four-year deal earlier in the day and ran on the field to join teammates as they stretched out to start practice.
Agent Josh Luchs declined to discuss terms of the deal for Henry, the 50th draft pick overall.
Henry will compete with veteran Chris Brown and LenDale White, last year's second-round pick, for the starting job. Travis Henry, who ran for 1,211 yards last season, now is in Denver after being released in March so the Titans could avoid an $8 million bonus.