Murphy, from Cork, 48, and his wife, artist Yvonne McGuinness, will refurbish The Phoenix Cinema in Dingle, Co Kerry, south-west Ireland, next year.
The venue, which has been used as a movie theatre and dance hall, had been in operation for more than 100 years, and had been on the market for three years before McGuinness and Murphy bought the building.
"I've been going to see films at The Phoenix since I was a young boy on summer holidays," Murphy said.
"My dad saw movies there when he was a young man before me, and we've watched many films at The Phoenix with our own kids. We recognise what the cinema means to Dingle."
The town centre cinema is the only one in the tourist area of the Dingle Peninsula, in the Ring of Kerry. The closest other movie theatres are miles away in Tralee and Killarney.
Michael O'Sullivan, who bought The Phoenix in 1978, ran the venue until the COVID-19 pandemic, when it was shut during Ireland's lockdown.
They cited rising costs, falling attendance and challenging exhibition terms.
McGuinness said. "We want to open the doors again, expand the creative potential of the site, re-establishing its place in the cultural fabric of this unique town."
The Phoenix Cinema has also hosted the Dingle International Film Festival, which Murphy has attended, as well as independent and foreign language films, and a Tuesday night film club.
The cinema was built by brothers Jimmy and Johnny Houlihan and opened in 1919.
After fires in 1921 and 1938, the venue was reconstructed twice. In the second rebuild the art deco facade, phoenix floor mosaic and name were added.
Guitarist Rory Gallagher performed there, and the David Lean-directed film Ryan's Daughter, made in the area, was shown.
A campaign to save it was launched when it shut three years ago.
Murphy won an Oscar this year for his performance in Oppenheimer, is best known for portraying gangster Tommy Shelby in the BBC drama Peaky Blinders, which debuted in 2013 and for which he has been nominated for a TV Bafta.
Peaky Blinders is to return with a Netflix movie, also starring Barry Keoghan.