Upon release, Brandy received generally positive reviews from music critics, who complimented Norwood's appearance, as well as the album's timeless appeal. It became a commercial success as well. While initial sales were slow, the album reached the top 20 of the US Billboard 200 was certified four-times platinum by the Recording Industry Association of America (RIAA), selling over two million copies in the United States. It experienced similar success in Australia and Canada, where it was platinum and gold respectively. Worldwide, the album has sold over six million copies.
Four singles were released from the album, two of which became number-one hits on the BillboardHot R&B Singles. "I Wanna Be Down" was chosen as the album's lead single, reaching the top ten in the United States and the top 20 in Australia and New Zealand. The song was critically lauded, and was regarded as a standout track on Brandy. The album's second single, "Baby" was also well received and charted even higher. With the following two singles, "Best Friend" and "Brokenhearted" also reaching the top ten in the US, Norwood established herself as one of the most successful of the new breed of urban R&B female vocalists to emerge during the mid-to late 1990s. It also garnered Norwood two Grammy Award nominations for Best New Artist and one for the album's second single, "Baby" for Best Female R&B Vocal Performance at the 38th Grammy Awards in 1996.
In 1990, Norwood's talent led to a binding oral contract with Teaspoon Productions, headed by Chris Stokes and Earl Harris, who obtained her gigs as a backing vocalist for their R&B boy band Immature. The same year, Stokes arranged the production of a demo tape which was handed over to Atlantic Recording Corporation executives. While they liked the material, they found Norwood too young at age 11 and told her to come back when she was 14. In 1993, amid ongoing negotiations with East West Records, Norwood's parents organized a recording contract with Atlantic after auditioning for the company's director of A&R, Darryl Williams. Norwood subsequently dropped out of Hollywood High School later and was tutored privately from tenth grade on.
During the early production stages of her debut on the Atlantic label, Norwood was selected for a role in the ABC sitcom Thea, portraying the 12-year-old daughter of a single mother played by Thea Vidale. Broadcast to mediocre ratings, the series ended only eight months after its premiere. Norwood appreciated the cancellation of the show as she was unenthusiastic about acting at the time and the taping caused scheduling conflicts with the recording of her album, stating: "I felt bad for everybody else but me. It was a good thing, because I could do what I had to do, because I wanted to sing [...] When Thea was canceled I was like, ‘Okay, I can now put all my focus into my album’." Atlantic consulted newcomer Keith Crouch to work with Norwood on the bulk of the album. Norwood noted that her collaboration with Crouch "was very important for me as a young artist. At the time he was not trying to be like anyone else on radio. He was all about his own sound. But what I really loved about Keith is he gave me real music. He didn’t give me teenybopper records. It was age appropriate, youthful records, but it was still real music. We had a great connection." While Crouch would provide the core sound of the album, Norwood also worked with all-male R&B group Somethin' for the People and Damon Thomas on some tracks. A then 16-year-old Robin Thicke scored his first co-writing credit on the album with "Love Is on My Side".
In his review for AllMusic, Eddie Huffman wrote that "this teenage R&B singer hit the Top Ten late in 1994 with "I Wanna Be Down", a representative track from her solid debut album. Brandy knows her way around a hip-hop beat, layering tender-tough vocals over spare arrangements like a lower-key Janet Jackson or a more stripped-down Mary J. Blige. Good songs and crisp production make Brandy a moody, moving success." In 2007, Vibe rated Brandy among the 150 most essential albums since its launch. The magazine found that "Brandy's debut is slow, deliberate, and naive — not for lack of accomplishment, but because the best moments here sound as wide-eyed and new as a first date."
People compared the effort with Aaliyah's debut album Age Ain't Nothing but a Number, which was released four months prior, writing: "While everything about Aaliyah screams here-and-now, Brandy's well-groomed blend of gently lilting hip hop and pop-soul has a more timeless appeal. With the poise and sassy confidence of a diva twice her age, Brandy mixes her love songs with tributes to her little brother ("Best Friend"), God ("Give Me You"), the perfect man ("Baby") and older crooners like Aretha and Whitney ("I Dedicate"). While this isn't groundbreaking stuff, Brandy has the pipes to become more than the latest teenage next-big-thing." Anderson Jones from Entertainment Weekly was less enthusiastic with the album. He gave the album a C rating and considered it as: "An album that seems based on the philosophy 'If Aaliyah can do it, why can't I?' except that in singing about best friends, heroes, and puppy love instead of about making love, teen actress Norwood (TV's Thea) acts her age. A premature effort, at best." In his Consumer Guide, Robert Christgau gave the album a "neither" score, and said it "may impress once or twice with consistent craft or an arresting track or two. Then it won't."
Serving as an inspiration for other artists, American neo soul singer Erykah Badu revealed on Twitter that her 1997 debut album, Baduizm, was partly influenced by Brandy, tweeting “Brandy's first album was one of my inspirations when writting Baduizm. I looove that album [...] songs i liked were "I Wanna Be Down" and "Always on My Mind"... nice." Fellow neo soul artist Jill Scott particularly praised the songs "Sunny Day" and "Always On My Mind" saying "I listen to her shit all the time".  Pop group Karmin's song "Brokenhearted" was inspired by Brandy's song of the same name.