"Frank de Boer is the new Nerazzurri coach," the Serie A club said on its Twitter page, followed by the hashtag #WelcomeFrank.
De Boer, 46, who left Ajax at the end of last season, touched down in the northern Italian city of Milan late on Monday to take over from Mancini, who left amid reports the club's new Chinese owners wanted fresh blood at the helm.
Inter said the new coach would be unveiled at a press conference at 2pm (1200 GMT).
"De Boer will join the Nerazzurri on a three-year contract and will take charge of first team training this afternoon," the club said in a statement.
The Dutchman, the most capped outfield player in the history of the Netherlands national team, had been linked with Premier League clubs Southampton and Everton before those positions were filled.
At Inter he will have under two weeks to sign more players before the Serie A season starts against Chievo on August 21st.
"Hello Inter fans. I'm very happy to be here and I hope to see you soon," he said in a video posted by the club as he arrived in Italy.
The club said he "brings with him a wealth of international experience having played at the highest level for both club and country".
At club level for Amsterdam's AFC Ajax he lifted five Eredivisie titles, the Uefa Champions League trophy, the Uefa Cup, the UEFA Supercup, and the Intercontinental Cup. He also played for Barcelona, Galatasaray and Rangers.
As head coach of Ajax, De Boer won four straight Eredivisie titles between 2011 and 2014.
Mancini said his farewells to the blue and black stripes of Inter Milan on Monday after failing to usher the club back into the Champions League and reportedly falling out with the owners over transfers.
The 51-year-old had been coach for two years, having previously led Inter to three league titles and two Coppa Italias during his first spell in charge between 2004 and 2008.