The forward, who signed yesterday on his 20th birthday, won gold with Brazil at the Rio 2016 Olympics, and has already played four seasons with Santos, scoring 12 goals in 28 appearances last campaign.
The news comes as very little surprise as Gabigol had actually undergone a medical at Inter last week, but had to fly home amid rumours Santos would only let him leave in January 2017.
The deal is now complete and the young striker will meet up with his new teammates after the international break.
Despite his age and relative inexperience in Europe, he is confident he has the ability to make the step up to the Italian Serie A.
"I liked the talks I've had with them, both the Coach and the players. I'm going there to help Inter," Gabigol told reporters.
"Here at Santos I learned many things, not only as a player but as a person. This is my home, as I've been here for 10 years.
"I like having pressure and feeling challenged, and for me this is just another challenge. The Italian championship is very competitive, and full of great teams.
"I'm more than ready to go and play in Europe. I'm going to go with my family and friends. And there are great Brazilian players in Italy too.
"It's a new challenge and I'm anxious to get started."