The 38-year-old became a free agent following the expiry of his contract with Sekhukhune United at the end of last season.
Although there was a possibility of a late U-turn that would have seen him remain with Babina Noko, the deal never materialised, paving the way for his move to Stellies.
Grobler is expected to sign a one-year contract, reuniting with coach Gavin Hunt, who previously worked with the prolific forward at SuperSport United.
Indications are that Grobler took time to weigh up his future, with the prospect of relocating from Gauteng and interest from AmaZulu also factors in his decision. However, Hunt's influence is understood to have played a significant role in convincing him to continue his career in the Western Cape.
The experienced striker leaves Sekhukhune after two productive seasons in which he finished as the club's leading goalscorer in both campaigns – scoring 11 goals in all competitions during the previous campaign.
Injuries did limit his appearances last season, but he still managed to rattle the net before being sidelined during the end of season run-in. Grobler also joined an elite group of PSL-era forwards to have scored more than 100 topflight goals.
His arrival continues Stellenbosch's busy rebuild following the departure of several key players, including Langelihle Phili, who joined Kaizer Chiefs as part of a transfer agreement that also saw Given Msimango and Ashley du Preez move back to the Cape club. Faiz Abrahams is also expected to sign for Chiefs on a season long loan deal.
Grobler is expected to link up with his new Stellies teammates this week, although his match fitness will be assessed after missing pre-season following his departure from Sekhukhune.
Stellies next league game is away to Polokwane City in Seshego on Tuesday.