The 35-year-old makes the switch to the Beavers just over a week after Bath manager Gary Owers left to take the vacant Torquay United job.
Morgan notched ten goals last season and will be a valuable asset to Hampton, who currently sit 15th, six places below the Romans.
The former Plymouth Argyle striker has also played for Aldershot Town, Woking and Shrewsbury Town to name a few.
A statement on Bath's website read: "Following a 7 day approach to the Club, Marvin has decided to leave Bath City and sign for another club in Vanarama National League South.
"Marvin brought a presence to the team both on and off the pitch during his spell with us and we wish him well for the future."