Their screening of the 1980s Michael J Fox film went ahead at the Olympic Park in east London on Thursday.
The organisers have created an immersive experience using actors and replicas of buildings from the film.
Media reviews of the event have been positive, while it was also well-received by audience members.
Satisfied fans took to Twitter. "Seriously impressive," wrote Holly Hunter. "Incredibly ambitious and totally brilliant! Fantastic evening!"
Ally Sinyard said the screening was "so brilliant, especially when everyone got up and danced during Johnny B Goode".
And Kat Brown said the show was "really wonderful".
The "only downside(s) were food queues and the prom photos breaking down. Everything else pure joy", she added.
Their responses contrasted sharply with the hundreds of angry messages that ticket-holders posted on Secret Cinema's Facebook page last week when they discovered shows had been cancelled with just a few hours notice.
Tickets for the event cost Â£53.50 each and, encouraged by the organisers, many had spent more money on 1950s-style fancy dress.
Some said they had travelled from as far away as the United States to see the show and would not be able to re-book.
Despite the one-week delay in opening the show, reviews in the Independent and the Guardian both gave it four out of five stars.
"Sometimes the immersive experience was so good that it blurred the line between fiction and reality," said the Independent.
"So many audience members dressed up in 1950s clothes which were as authentic as those of the actors employed by the production, [so] that everyone was a co-contributor," wrote the Guardian.
The Evening Standard talked of a "celebratory mood" at the screening, and The Public Reviews blog said "scenes from the movie are recreated as they play out on the giant screen. All of these are masterful".
The set for the event included 1950s-styled burger bars and a replica of the clock tower that featured in the film.
There was also a record shop, comic shop and a barber's - for anybody who wanted to leave with a 1950s-style haircut.
Secret Cinema has opened its Back to the Future show a week after the opening night was cancelled at short notice.