They think they got lucky and hit the lottery.
The Titans are confident the move will translate into wins -- maybe even the missing piece that could deliver owner Bud Adams and coach Jeff Fisher their first Super Bowl.
Fisher, the NFL's longest-tenured coach, is known as a player's coach who holds his guys accountable. The Titans (5-3) are winning with a strong locker room hungry for the franchise's first postseason win since January 2004, which should keep Moss focused for their eight-game playoff push.
All reasons why, though no one else in the NFL wanted the 13-year veteran, the Titans feel Moss now is on the right team at the right time.
"This is a great opportunity for him," Fisher. "It's a fresh start. We've got a great locker room. They'll accept him. I'm confident he'll accept his new teammates as well."
Fisher himself is the biggest reason this can work.
He has dealt with egos -- Adam Jones and Albert Haynesworth and running back LenDale White -- coaxing out big punt returns, interceptions, sacks and touchdowns before those players wore out their welcome in Tennessee. The Titans eventually traded away Jones and White, and let Haynesworth walk via free agency.
Now in his 16th full season, Fisher also has enough clout to make personnel decisions as he sees fit. Fisher is a former player with a good feel for when to practice longer or turn a session into a walkthrough, which his players notice.
Not that the Titans are expecting any issues.
They did their homework on Moss, including talking to backup quarterback Kerry Collins. Moss and Collins were teammates for a year in Oakland, and Collins calls him a great teammate. Fisher also talked to Moss himself and said the receiver is excited to come to Tennessee.
"We think that he can help us, and I'm looking forward to seeing him run under those deep balls," Fisher said.
That's where Moss fits best.
He gives offensive coordinator Mike Heimerdinger the best option he's had to throw downfield. The Titans have been trying to do just that the past few weeks, attempting to stretch the field for running back Chris Johnson. Kenny Britt had 225 yards receiving on Oct. 25, the best day in the NFL this year, and Nate Washington had a career-best 113 yards in last week's 33-25 loss to San Diego.
Vince Young is the NFL's top-rated passer at 103.1 for the first time in his career, though the Titans rank 24th with 187.6 yards passing per game. Moss is expected to change that.
"He should be a difference maker for the offense and other individual players on our offense," Heimerdinger said.
The biggest benefactor could be Johnson.
He is the NFL's third-best rusher with 721 yards, but defenses stack the line against him. And though the Titans are the NFL's second-highest scoring team (28 ppg), things were bound to get tougher for Johnson.
Britt is expected to miss four weeks with a hamstring injury, a league source told ESPN NFL Insider Adam Schefter.
"I know for a fact they can't put all those guys in the box with that guy out there," Johnson said Thursday in quotes shared by the team after a closed practice.
Johnson isn't the only player excited about the arrival of Moss and his 153 career touchdowns.
The Titans missed the playoffs last year and lost in their previous two postseason appearances, and they are a half-game back of Indianapolis (5-2) in the AFC South at their bye with five divisional games left down the stretch.
They expect Moss to be ready to work when they return to practice Tuesday after their bye week.
"We need to make sure we are here to play, we are here to win, and that is what it is all about," linebacker Will Witherspoon. "I think coach Fisher said it himself. Anytime you have a chance to improve the roster, you need to try to make that move if you can. I think they had the opportunity and took full advantage of it."
Though the man with the West Virginia drawl can be moody, snarling at reporters or responding with candor and wit, past teammates have nothing but good things to say about the 6-foot-4 receiver.
Even if Moss didn't give 100 percent, Minnesota quarterback Brett Favre said he was dangerous.
"So, did he hustle on every play? I don't know if Randy has ever hustled on every play. That's just Randy," Favre said. "But he knows what his value is. He figures, 'Heck, two guys follow me everywhere I go.' ... They may watch and say, 'He's jogging, jogging, jogging.' Boom! 70-yard touchdown."
Vikings receiver Greg Camarillo credited Moss with making him better. Adrian Peterson tweeted he knew Johnson was excited and that he enjoyed his time with Moss. Tom Brady still calls Moss a "great friend."
Saints fullback Heath Evans said Moss had young receivers in the weight room at 6 a.m., bugging coaches to open the doors early so he could start work.
"As an old teammate, any time I hear negative news about him it angers me because I know the guy," Evans said. "Listen, he's the type of guy you want on your team on Sundays."
That's the Moss the Titans believe they've got.
Tennessee tight end Bo Scaife said "Thank you Jesus" once they landed the veteran.
"I hope he's mad at those other teams passing him up, and he comes in and gives us the best eight games of his career," Scaife said.
Information from The Associated Press contributed to this report.