The Argentine defender is determined to fight for silverware with the Nerazzurri, while Samir Handanovic also spoke of his delight at securing a move to the Giuseppe Meazza
The 27-year-old is expected to complete his switch to the Italian giants on Friday, and the centre-back is relishing the prospect of being in the running for silverware once more.
"I am very happy to be here, and I want to win trophies just like I did at Boca Juniors in the past," Silvestre was quoted as saying by Corriere dello Sport.
"I'm pleased to join Inter because a lot of my compatriots already play here. I will get the chance to compete for silverware again."
Goalkeeper Samir Handanovic, who is also set to join the Nerazzurri in the immediate future, was also delighted with his move, claiming that Inter showed the most intent in signing him.
"The contract has been taken care of now and I'm very pleased with this move," he added.
"Other clubs were interested in signing me as well, but Inter showed the strongest desire to sign me. I don't know yet which number I'll be wearing."
The 27-year-old Slovenia international will join the Milanese club for €11 million, with Italy Under-21 full-back Marco Faraoni heading in the opposite direction to Udinese on a co-ownership basis.