The winger, who is a free agent after his contract with Blackpool expired, spent the second half of last season on loan at Crystal Palace but made just eight appearances for Tony Pulis’ side.
"For me it is an extraordinary adventure,” Ince told reporters.
“When I was five years old, I lived the atmosphere of San Siro because my father played here. It’s a dream.
“I have spoken many times with [Inter president Erick] Thohir, he wants to build an Inter side that is strong and competitive in Italy and in Europe.”
The 22-year-old arrived in Milan late on Sunday evening with his father Paul, who spent two seasons at the Serie A club during his playing career.
"For me is amazing return to Italy after all these years, to find this club and many friends at the airport,” Paul Ince told Sky Sports.
“I have an excellent relations with [former Inter president Massimo] Moratti. I'm very fond of the Inter story and I hope that my son will be part of that.”