As reported by Goal, the initial loan deal is worth €6 million (£5.4m/$6.8m) and the agreement includes an option for the Nerazzurri to sign the 23-year-old permanently for a further €42m plus a percentage of any future transfer.
Keita scored eight goals in 23 Ligue 1 appearances for Monaco but has been given the green light to move to Inter.
Speaking to La Gazzetta dello Sport, Keita's agent Roberto Calenda praised Monaco for allowing the 23-year-old to move back to Italy.
"Monaco should be thanked," Calenda said. "They gave Keita back his smile, his serenity and his carefree feeling after years of tension and promises made and never kept by Lazio's management.
"I'm not surprised they let him leave: the deal will benefit everyone. The player still has the desire to explode in this country, where he grew up as a footballer. At 23, it's the perfect time to do it."
Keita made a single appearance for Senegal at the World Cup, starting his country's 1-0 loss to Colombia in the group stage.
He now becomes the latest man to join Inter in a busy transfer window for the Nerazzurri, after Lautaro Martinez, Radja Nainggolan, Stefan de Vrij, Kwadwo Asamoah, Sime Vrsaljko and Federico Di Marco.