In an announcement posted on Inter’s website, Inter president Massimo Moratti expressed “complete satisfaction” with the choice.
Gasperini, a former Genoa coach, became the leading candidate after Inter failed to lure Fabio Capello from England and Chelsea hired Andre Villas-Boas.
Inter said he will sign a two-year contract.
Gasperini, 53, led Genoa to promotion from the second division in 2007 and qualification for the Europa League with a fifth-place finish in Serie A in 2009. He was fired by Genoa in November.
Inter will announce the date of his official presentation to the media at a later time.