The 30-year-old wing-back, who can also operate on the right of midfield, becomes a free agent next month and was signed on a three-year contract under the Bosman ruling.
Eranio was wanted by Monaco and Porto, while Milan offered him another two-year deal. But Eranio made his mind up after a visit to Derby and Smith said: "He liked what he saw, the new stadium and the potential. I think it was the honesty of the club that sold it to him. We have signed one of the best wing-backs in Europe and it's very exciting for the fans and for me."
Eranio joins a growing band of Italians who have joined Premiership clubs in the last year and had a blunt message for anyone who questions his commitment. Speaking through an interpreter, he insisted: "I was on Genoa's books for 15 years and then spent five years with Milan and it was me that wanted a three-year contract at Derby."
Eranio would have been valued at about pounds 4m under contract and Smith, added: "We have signed a world class player from one of the biggest clubs in the world on a free transfer, and you can't get better value than that."
Derby also completed the pounds 500,000 signing of the Birmingham midfielder Jonathan Hunt. Steve Castle, freed by Birmingham, has joined Peterborough. Meanwhile, the Birmingham captain, Steve Bruce, has emerged as a leading contender for the managerial vacancy at Stoke.
The Sunderland manager, Peter Reid, hopes to complete the pounds 1m signing of a Dutch goalkeeper, Edwin Zoetebier, today. The Volendam player arrived on Wearside with his agent last night to finalise personal terms.
The former Dutch under-21 international, also being watched by Rangers, is keen to come to England and should get his wish after the clubs agreed a price. Signing Zoetebier, whose name means sweet beer in Dutch, will cheer up Reid after missing out on Blackburn's Shay Given, who is set to join neighbours Newcastle. But the arrival of Zoetebier will mean the end for the popular Frenchman Lionel Perez. He will be allowed to go for a reasonable fee once the Dutchman signs.
Chris Waddle will not be part of Sunderland's attempt to regain their Premiership status next season. Reid has told the 36-year-old former England winger that his contract, which runs out at the end of June, will not be renewed.
Reid told Waddle, who joined Sunderland from Bradford in March in a pounds 75,000 deal, that he had done a magnificent job for the club during his brief stay. Waddle played seven games for Sunderland but was unable to prevent them from being relegated to the First Division.Reuse content