The deal is worth $20 million, with an additional $3 million in incentives, according to NFL Network's Mike Garafolo.
Lewis spent the past three seasons with the New England Patriots, helping the team win a Super Bowl in 2016.
The 27-year-old is coming off a career year in which he rushed for 896 yards and six touchdowns, and added 32 receptions for 214 yards and three scores through the air.
Lewis will now form a strong running back tandem with Derrick Henry.
Another former Patriot, cornerback Malcolm Butler, will also join the Titans, as he agreed to a five-year, $61-million contract.