The singer sued the brand's parent company Arcadia for $5million (£3.3m), accusing the fashion chain of attempting to pass off the garments as being approved by her.
The t-shirts bore a photo of Rihanna taken during a video shoot in Northern Ireland 2011, an image that was taken by a freelance photographer "without her permission".
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Judge Mr Justice Birss ruled in the singer's favour after a hearing in London.
"There is no such thing as a general right by a famous person to control the reproduction of their image," he said during a two-minute judgement.
"The mere sale by a trader of a t-shirt bearing an image of a famous person is not an act of passing off.
"However, I find that Topshop's sale of this t-shirt was an act of passing it."
Rihanna's lawyers had accused the fashion chain had duped fans and may have damaged her reputation. They also said the picture was "very similar" to images used on CD sleeves for one of her albums.
Martin Howe QC, for Rihanna, told the court, "Rihanna is one of the world's most famous musical performing artists. She needs little introduction.
"Like most well known contemporary performing artists, she engages in merchandising, and like most such performing artists, it represents a significant part of her revenue stream.
"In 2012, Topshop sold a T-shirt displaying a clearly recognisable image of Rihanna taken when she was on a video shoot. She was wearing her makeup and hairdo for the video shoot, and very similar images of her appeared on her CD inlay (for the album Talk that Talk.)
"A substantial number of people buying, or even seeing, those T-shirts would think they are approved or somehow connected with Rihanna, when, in fact, they were not approved of or connected with her at all."
Topshop, meanwhile, had disputed the claims, saying that the 25-year-old was making an unjustifiable bid to establish a "free-standing image right" over use of her picture in the UK.