The 53-year-old Italian, sacked by mid-table Serie A side Genoa in November, was named Inter boss last week to succeed Leonardo after a string of more high-profile names turned down approaches.
"I'm so proud to be here at Inter," Gasperini told Inter Channel on his first day at work on Monday.
"It came as a huge surprise but now I am very ambitious and determined to do well, to have a big season."
"[His praise] motivates me even more to have a successful season, which is what I intend to do by creating a very close-knit and strong group," Gasperini said.
"But the foundations with those characteristics are already in place."
Top players Samuel Eto'o, Wesley Sneijder and Maicon have all been linked with moves away while goalkeeper Emiliano Viviano looks set to return from a spell at Bologna and Santos full-back Jonathan is close to joining, media reports have said.
