The actresses starred as 1950s and '60s pals and roommates Laverne DeFazio and Shirley Feeney, workers in a Milwaukee brewery. The sitcom aired from 1976 to 1983 on ABC.
"Sam & Cat" features Jennette McCurdy and Ariana Grande as friends who start a baby-sitting business.
Nickelodeon says Marshall and Williams will start filming on Wednesday. They play characters involved in a decades-old feud, tweaking the long-ago rumors of a "Laverne & Shirley" rivalry.
"Sam & Cat" creator Dan Schneider says it was an honor to write for what he called TV's" funniest female roommates" ever.