His departure follows Saturday's humilating 7-1 defeat at Swansea City, which left the side languishing in the relegation zone.
Tinnion met with Robins chairman Steve Lansdown on Sunday, and his resignation was accepted.
Assistant Keith Millen will take control of first team duties as caretaker boss.
Landsown said: "I am very disappointed Brian Tinnion has decided to stand down from the position of first team manager.
"However I fully understand his frustration at recent results, and the pressure that has been placed upon him and his family.
"During his time as manager Brian has worked tirelessly on all aspects at the football club. Not just in first team selection and management, which the general public will see, but also the devleoplment of our younger players.
"I place on record my thanks to Brian and would like to wish him all the best for his future career."
Tinnion is the first League One manager to lose his job this season, but Nottingham Forest boss Gary Megson and Swindon chief Andy King have also faced calls for their resignation from supporters.