The 20-year-old was spotted playing in the South American Under-20 championship in Argentina, and is now believed to be in Italy to secure a passport.
Laxalt, who plays for Primera Division Uruguaya side Defensor Sporting, will not be able to make his debut until next season, but will still train with the squad.
"It's all done, Diego's paperwork is in order and he will be an Italian citizen tomorrow," his agent Vincenzo D'Ippolito told Itasportpress.
"Inter will only be able to register him as their player in the summer, but in the meantime the lad can train with the Nerazzurri squad."
The midfielder is expected to pen a deal until June 2018.