The company also separated the roles of chairman and CEO, naming lead independent director Domenico De Sole chairman, it said on Monday.
Sotheby's said in November that Ruprecht would step down once a successor was found. The announcement followed months of demands for big changes at the company from activist investors including Daniel Loeb.
Loeb, whose hedge fund Third Point was Sotheby's largest shareholder as of May 2014, joined the centuries-old auction house's board last year.
Smith will take over at Sotheby's from March 31, about a year after he joined Madison Square, the owner of New York Knicks and New York Rangers.
Activist investor Marcato Capital Management, Sotheby's second-largest shareholder, said in February that the company should buy back $500 million of shares immediately and replace its Chief Financial Officer Patrick McClymont.
Sotheby's said earlier last month that there would be no return of capital until it found a new CEO.
Activist investors have called for other major changes at Sotheby's, including the sale of its headquarters on the Upper East Side of Manhattan.