Eriksen had been angling for a move from North London since the summer after making his intentions clear of not wanting to extend his six-and-a-half-year stay at the club.
The 27-year-old Dane had just six months remaining on his contract and would have been a free agent in the summer.
Eriksen joined Tottenham from Ajax Amsterdam in 2013, going on to make 304 appearances and scoring 69 goals.
Eriksen becomes the fifth Premier League player to move to the San Siro since Antonio Conte was appointed Inter Milan boss last summer.
Romelu Lukaku and Alexis Sanchez joined from Manchester United at the start of the season while Ashley Young and Victor Moses have transferred from Old Trafford and Stamford Bridge in recent weeks.
Speaking to InterTV once the move was confirmed, Eriksen said: 'I couldn't wait to get there, being here is beautiful and I'm happy to be a new Inter player.
'I am very excited and I can't wait to get to know the fans, I have already had the opportunity to feel their warmth, it was a fantastic welcome. I feel great.
'Honestly I'm not one who cares a lot about numbers but I know that people like them and testify that I did a lot well in England.
'Now the time has come to take on a new challenge, I am very happy to be able to play in Serie A and with a great club like Inter, it is a fantastic club.'
Inter Milan are three points behind leaders Juventus in the race for the Scudetto.
