The Two Pints Of Lager And A Packet Of Crisps star will play Reese Witherspoon's movie character Elle Woods, the Daily Telegraph reports.
Smith said: "It's a dream come true. I can't believe I got it.
"When I knew I was auditioning [boyfriend James Corden] bought the CD and we sung the duets together. He wanted to be in it but I don't think he's right for the part."
She added that the story was "about being true to yourself", and suggested that middle-aged men would "secretly enjoy" the production when going to watch it with their wives and daughters.
The Broadway musical production of Legally Blonde closed last autumn after an 18-month run.