The two athletes had been competing in the 3000m women's-track final - which Decker, who was running for the US, had been widely tipped to win.
But she fell after a collision with Budd, who was part of the British team.
Budd, who was born in South Africa and aged 17 at the time of the race, was later accused of tripping her up.
The crowd's hostile reaction after Decker's fall caused Budd, who famously ran barefoot and had been winning the race, to finish seventh.
Decker, who had fallen into the infield grass clutching her right thigh, was carried from the track in tears.
Budd had already received international attention after her application for British citizenship was fast-tracked earlier in 1984, in time for her to compete at the Los Angeles games.
As a South African, Budd would have been ineligible to compete as the country had been banned from international sport because of its policy of apartheid.
The new film will feature archive footage as well as new interviews with Budd, Decker and others who were close to the events leading up to the race.
On reuniting with Decker in the documentary, Budd commented: "I knew making this film would be opening up the black box in my mind which I haven't opened since that day. I thought it was time."
Decker added, "I still think about that race every day. Making this film has been cathartic."
The 90-minute film, called The Fall, will premiere on Sky Atlantic on 29 July.

Asha Philip, Desiree Henry, Dina Asher-Smith and Daryll Neita ran a British record of 41.77 seconds in Rio's Olympic Stadium.
The US, who only qualified for Friday's final at the second attempt after dropping their baton, won in 41.01, the second-fastest time in history.
Silver medallists Jamaica ran 41.36.
Jamaica's Elaine Thompson narrowly missed out on matching compatriot Usain Bolt's sprint treble after her victories in the 100m and 200m.
"Wonderful experience. My first Olympics. Two golds, a silver, I can't complain," she said.
GB's first medal in the event since winning bronze at Moscow 1984 capped a remarkable reversal in fortunes after they failed to reach the final at London 2012.
Philip, the oldest member of the quartet at 25, said: "We came here to get a medal and we delivered. We had a lot of pressure to get this, but we had so much trust and faith in these girls."
Henry, 20, said: "I cannot believe it. This was my first Olympics and I wanted to go out and enjoy it but also to get a medal. To do it I had tears in my eyes. Thank you to everyone who has made this happen."
Asher-Smith, also 20, said: "We have worked unbelievably hard. Out of all the teams I think we worked the hardest. This is for the entire nation."
Daryll Nieta, 19, said: "I am speechless. I am so proud of our team. We absolutely smashed it."
Find out how to get into athletics with our special guide.
Chief sports writer Tom Fordyce
Fabulous from the GB quartet. Having spent the day with them as they trained at Loughborough, there was no missing that this is the tightest of teams - true friends, proper racers. Philip in the mother role, Asher-Smith as head girl, Henry the loud one, Neita the kid. Together history makers.
Tianna Bartoletta, Allyson Felix, English Gardner and Tori Bowie were allowed to compete in the final after running again - on their own - following Thursday's semi-final.
The baton was accidentally knocked out of Felix's hand by Brazil's Kauiza Venancio as she prepared to hand over to Gardner for the third leg.
The US successfully appealed, and ran only two tenths of a second short of the world record at the second attempt.
Bartoletta and Felix were part of the US team that clocked 40.82 to win at London 2012, and Felix has become the first woman to collect five athletics gold medals.
"It's very special. It was great to join these women tonight. It's just a very unique experience," Felix said of her milestone.
Subscribe to the BBC Sport newsletter to get our pick of news, features and video sent to your inbox.
Zola Budd and Mary Decker are to be reunited in a new documentary for the first time since their famous collision at the Los Angeles Olympics in 1984.
[NEXT_CONCEPT]
Great Britain won an Olympic medal in the women's 4x100m relay for the first time since 1984, claiming bronze as the United States retained their title.