The musical, which opened on Broadway in 1981 and was filmed in 2006, has taken 35 years to reach the West End.
Sonia Friedman partly attributes the delay to actors not being available to populate its predominantly black cast.
"Thankfully, shows like The Lion King have meant many more people of colour are now working in theatre," she said.
"When Dreamgirls opened [in New York] 35 years ago, it would have been very hard to cast it here at that time," the producer continued.
"We now have a fantastic talent pool and will be able to keep it running for years and years because of the talent that is out there."
The Lion King opened in 1999 in London and still plays to full houses at the Lyceum Theatre, 17 years on.
Several members of Dreamgirls' ensemble have appeared in the show there, or in other stagings of the Disney musical.
Freidman also cited the specific demands placed on the show's lead actress as another reason why Dreamgirls has taken so long to cross the Atlantic.
Dreamgirls tells of a black female singing trio, reminiscent of The Supremes, who fight to make their mark in '60s America.
The 2006 film, starring Beyonce and Eddie Murphy, was many Britons' first exposure to the Tony Award-winning show.
Jennifer Hudson won an Oscar, a Bafta and a Golden Globe for playing Effie White, the threesome's most gifted and volatile member.
The role - which Friedman says is like "climbing Everest and doing a marathon at the same time" for a performer - is played in London by Amber Riley.
Riley, best known for playing Meredith Jones in US TV show Glee, was in tears as she took her bows at end of Wednesday's opening night.
"Some nights it's like that," she told the BBC News website. "I get so overwhelmed and caught up in the story."
Riley, who is making her West End debut in the production, said the part of Effie was "the role of a lifetime".
"She starts really young and ballsy and she gets to be vulnerable, and then she gets to be an adult," the 30-year-old explained.
"I get to show her whole entire journey, and I've never really gotten to share that arc before."
Reviews of the show have praised the US actress, with The Guardian describing her as "a notch above... on a stage of great singers".
Its critic Lyndsey Winship said that her "huge and effortless voice... rips through the auditorium".
"Without question, Riley is the biggest reason to buy a ticket," writes Dominic Cavendish in the Telegraph.
Casey Nicholaw's "slick" and "tinselly" production, he continues, offers "tremendous gusto of soul and gaiety of spirit".
The Mail's Quentin Letts says the show "has great costumes and incessant dancing" and is "likely to be a hit".
The Times' Ann Treneman, however, thinks "it doesn't deserve to be" one - as its plot is "far too skimpy" and its singing "way too loud".
Riley's Glee co-star Chris Colfer and comedian Sir Lenny Henry were among the audience at the Savoy Theatre on Wednesday.
Sir Lenny has been a vocal campaigner for more representation of black, Asian and minority ethnic (BAME) people in the broadcasting industry.
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The producer of Dreamgirls has said its belated London transfer might not have happened had shows like The Lion King not helped foster black acting talent.