The actress, who has tasted minor success as a singer, admits she fell for Sinatra's voice when she was a toddler and still swoons whenever she hears one of Ol' Blue Eyes' songs.
She explains, "When I was a little kid, my favourite singer was Frank Sinatra. I thought that maybe when I grew up I could sound like Frank Sinatra.
"He was a huge part of my childhood and my excitement about singing and music when I was a kid…I remember having this Fisher Price little tape player thing. It had a microphone attached to it... I used to pop in the Frank Sinatra cassette and I became absolutely obsessed with the Best of Frank Sinatra, and I would sing into the microphone with it."
Picking her top tunes for a guest hosting stint on Los Angeles public radio network KCRW, Johansson also revealed Beach Boys star Brian Wilson once made her cry at a concert by performing In My Room: "I don't think that I've ever cried that hard at a concert before. I find his whole story very touching and this song, really, the lyrics were very poignant.
"I think that a lot of people have that when they're a teenager, where their room is really sort of their safe haven and they can hold all their secrets there. Certainly that was my experience, anyway, so this song really spoke to me when I was a teenager."