The 20-year-old Argentine had been linked with a move to Europe for some time amid his strong performances for Racing Club.
He admitted in March that he was all but set to join the Nerazzurri, confirming that there were "final details to be worked out".
Negotiations have come to an end, however, and the Argentina international will sign a contract with Luciano Spalletti's side.
Martinez netted an impressive 17 goals in 24 games in all competitions for Racing this season, after scoring eight in as many games in 2016-17.
He made his Argentina debut when he came off the bench in a 6-1 defeat to Spain in March for his only appearance to date. Martinez will not be travelling to the World Cup this summer, however, having failed to make it into Jorge Sampaoli’s squad for the tournament in Russia.
Martinez has been likened to Manchester City star Sergio Aguero by Hernan Crespo because of his eye for goal and intelligence.
"He is very good and can play in many roles; on the wing, as a secondary striker or up top by himself as the main striker," Crespo said in March. "He has a knack for scoring and he's an intelligent guy.
"Coming to Inter isn't easy, he'll need to be helped and protected. Then hopefully he can show all of his qualities from the beginning, but it won't be a disaster if he needs a little time to settle in.
"He can play with Icardi, I don't think there will be any problems. He reminds me a little bit of Aguero in some ways, like with his low centre of gravity, but he's Lautaro Martinez."