The Anthony's chain of food outlets included restaurants in the city's Corn Exchange building and a patisserie in the Victoria Quarter.
The firm was founded in 2004 by chef Anthony Flinn and his father, also called Anthony Flinn.
Lines Henry Ltd have been appointed as administrators and said there was not enough money for the firm to continue trading.
Michael Simister, of Lines Henry, said: "It is sad when such a well-known business runs into difficulties.
"Unfortunately, the business has had to close, with the loss of 70 jobs, because there is not enough money available to continue trading."
He added despite good reviews the business had struggled with increased competition and difficult economic conditions.
The failure of a restaurant business in Leeds has led to the loss of 70 jobs.