Esor joined the Dar es Salaam club from Nigeria Professional Football League champions, Rivers United.
The 25-year-old linked up with Rivers United from local rivals, Go Round FC in January, 2019.
Esor scored scored 11 goals and provided five assists in 83 league appearances for Rivers United.
The talented midfielder played a key role as Stanley Eguma’s side claimed the NPFL title for the first time last season.
“Nelson Esor has joined Simba FC of Tanzania,” the club tweeted.
“A model professional. A credit to Rivers United.
“We thank you Esor for your contribution to our club during your stay with us.
“Everyone at Rivers United wishes Nelson Esor and his family all the very best in their new chapter,” added the Port Harcourt club.