Born in Flushing, New York, Weinstein and his younger brother, Bob, grew up in a Jewish family in New York City, residing in a housing co-op named Electchester. He graduated from John Bowne High School, and then the State University of New York at Buffalo.

Weinstein, along with his brother Bob Weinstein, and Corky Burger independently produced rock concerts as Harvey & Corky Productions in Buffalo through most of the 1970s. Both Weinstein brothers had grown up with a passion for movies and they nurtured a desire to enter the film industry. In the late 1970s, using profits from their concert promotion business, the brothers created a small independent film distribution company called Miramax, named after their parents - Miriam and Max. The company's first releases were primarily music-oriented concert films such as Paul McCartney's Rockshow. In the early 1980s Miramax acquired the rights to two British films of benefit shows filmed for human rights organization Amnesty International. Working closely with Martin Lewis, the producer of the original films, the Weinstein brothers edited the two films into one movie tailored for the American market. The resulting film was released as The Secret Policeman's Other Ball in May 1982 and it became Miramax's first hit. The movie raised considerable sums for Amnesty International and was credited by Amnesty with having helped to raise its profile in the US.

The Weinsteins slowly built upon this success throughout the 1980s with arthouse films that achieved critical attention and modest commercial success. Harvey Weinstein and Miramax gained wider attention in 1988 with the release of Errol Morris's documentary The Thin Blue Line which detailed the struggle of Randall Adams, a wrongfully convicted inmate sentenced to death row. The publicity that soon surrounded the case resulted in the release of Adams and nationwide publicity for Miramax. In 1989, their successful launch release of Steven Soderbergh's Sex, Lies, and Videotape propelled Miramax to become the most successful independent studio in America.

Also in 1989, Miramax released two art-house films, The Cook, the Thief, His Wife & Her Lover and director Pedro Almodóvar's film Tie Me Up! Tie Me Down!, both of which the MPAA rating board gave an X-rating, effectively stopping nationwide release for these films. Weinstein sued the MPAA over their rating system, although his lawsuit was later thrown out; the MPAA, however, agreed to introduce the new NC-17 rating following this episode.

Miramax continued to grow its library of films and directors until, in 1993, after the success of The Crying Game, Disney offered Harvey and Bob $80 million for ownership of Miramax. Agreeing to the deal that would cement their Hollywood clout and ensure that they would remain at the head of their company, Miramax followed the next year with their first blockbuster, Quentin Tarantino's Pulp Fiction and distributed the popular independent film Clerks.

Miramax won its first Best Picture Academy Award in 1996 with the victory of The English Patient (Pulp Fiction was nominated in 1994 but lost to Forrest Gump). This started a string of critical successes that included Shakespeare in Love and Good Will Hunting.

On March 29, 2005, it was announced that the Weinstein brothers would leave Miramax on September 30 to form their own production company, named The Weinstein Company with several other media executives, reportedly, directors Quentin Tarantino and Robert Rodriguez and Colin Vaines who had successfully run the production department at Miramax for ten years and moved with the brothers to head development in the Weinstein company.

The new studio immediately garnered Academy Award nominations for Transamerica and Mrs. Henderson Presents, and box office success through Hoodwinked and Scary Movie 4.

While lauded for opening up the independent film market and making it financially viable, Weinstein has been criticized by some for the techniques he has allegedly applied in his business dealings. Peter Biskind's book, Down and Dirty Pictures: Miramax, Sundance and the Rise of Independent Film, details criticism of Miramax's release history and editing of Asian films, such as Shaolin Soccer, Hero and Princess Mononoke.

Another example cited by Biskind was Phillip Noyce's The Quiet American, whose release Weinstein delayed following the September 11 attacks, due to audience reaction in test screenings to the film's critical tone towards America's past foreign policy. After being told the film would go straight-to-video, Noyce planned to screen the film in Toronto International Film Festival in order to mobilize critics to pressure Miramax to release it theatrically. Weinstein decided to screen the film at the Festival only after he was lobbied by star Michael Caine, who threatened to boycott publicity for another film he had made for Miramax. The film received mostly positive reviews at the Festival, and Miramax eventually released the film theatrically, but it was alleged that Miramax did not make a major effort to promote the film for Academy Award consideration, though Caine was nominated for an Academy Award for Best Actor.