The movie, which charts the tension between the war0time prime minister and allied leaders during the five days before the June 1944 D-Day landings, is being shot at locations across Scotland.
Starring Brian Cox in the leading role, it is set to hit the screens in January next year.
Ms Hyslop will make a keynote speech to the Scottish Screen Summit today, in which she will say ministers are committed to supporting Scotland’s screen sector.
It comes after she met the Churchill production team and watched filming at the set.
Ms Hyslop said: “Scotland is widely recognised as a location for international film and TV productions.
“The talent of the Churchill cast and crew highlights why Scotland is an attractive place to shoot large-scale productions.
“During my visit, I met three young Scottish crew members, including a trainee grip, costume trainee and a floor runner, to hear about their experiences working in the screen sector of Scotland.
“It’s vital that we continue to work together collectively to encourage fresh talent into the TV and film industry.”
The Salon Pictures production, directed by Jonathan Teplitzky, has received £250,000 from a £1.75 million fund administered by Creative Scotland and aimed at encouraging international productions to come to Scotland.
Producer Piers Tempest said: “We’ve been filming across 11 Scottish locations since May 23 and each one has proved unique.
“Scotland is a highly-attractive location for film makers with stunning backdrops.”