Eriksen will have a medical in Milan early next week before completing a four-and-a-half-year deal worth in the region of 20 million euros ($22 million).
The 27-year-old joined the Premier League club in 2013 from Ajax and has six months left on his contract.
Antonio Conte’s title-chasing Inter have already bought defender Ashley Young from Manchester United, with midfielder Victor Moses arriving on loan from Chelsea.
Last summer they signed Romelu Lukaku and Alexis Sánchez, the latter on loan, from Manchester United.
Inter are second in Serie A, four points behind Juventus, and play Cagliari on Sunday.
The Italian club last won Serie A in 2010.