The 22-year-old arrives at Huish Park for a second spell, having spent time with on loan with the club towards the end of the 2015/16 campaign.
Goodship, who was handed his EFL debut by Darren Way, scored the winner against Dagenham & Redbridge last February – a result which went a long way to securing Yeovil’s Football League status.
Eleven months on the young striker, who can play across the front three, joins up with Town once again after having his Cherries contract terminated by mutual consent.
After signing Goodship, Way said: “Brandon’s got an opportunity to get his career back on track. I thought he did extremely well under immense pressure last season.
"I don’t forget the goal he scored at Dagenham away which was crucial for the situation we were in, and many supporters witnessed some of the excellent performances he had – especially Mansfield away and Plymouth at home.
"It’s up to Brandon now to take this opportunity and again, he’s another one where the connections with Bournemouth seemed to have worked well."
Brandon will be available for Town’s trip to Wycombe Wanderers on Saturday, and will wear the number 19 shirt.
Everyone at Yeovil Town Football Club wishes Brandon all the best during his time at Huish Park.