Eriksen, 27, arrived in Milan on Tuesday to pass his medical and sign a contract that will run to 30 June, 2024.
The Denmark international spent six and a half years with Spurs but, with his contract set to expire at the end of this season, he had long been expected to leave.
Despite links with Manchester United and Real Madrid, among others, Inter has managed to bring the playmaker to San Siro.
In a statement in which they also announced the signing of Giovani Lo Celso on a permanent deal, Spurs said: "The club can also confirm the departure of Christian Eriksen after agreement was reached with FC Internazionale Milano for the Denmark international's transfer.
"He made 305 appearances for us following his move from Ajax in August, 2013, and scored 69 times.
"We wish Christian well for the future."
With his future in question, Eriksen had spent the first part of the season in and out of the Spurs team, his 20 Premier League appearances split evenly between starts and substitute outings.
His form unsurprisingly suffered as dip as a result as he mustered just two goals and two assists from those 20 games.
Fans had become increasingly critical of Eriksen's performances in recent times, with Spurs head coach Jose Mourinho acknowledging last week that the Dane had not been at his best despite insisting his application in training remained positive.
His form has not put off Inter, which will hope the signing helps to give it added impetus in the Serie A title race having fallen behind pacesetter Juventus since the turn of the year.
Antonio Conte's men are three points adrift of Juve after three successive league draws, the latest a 1-1 stalemate at home to Cagliari.
Eriksen is Inter's third signing of the month, with all three coming from Premier League sides after the arrivals of Ashley Young and Victor Moses from Manchester United and Chelsea, respectively.