A deal is expected to be concluded in the next few days for the 28-year-old Croatian international, and will likely come to £48m.
Personal terms had already been agreed with Perisic, although Inter had been completely unmoving on the size of the fee.
The Italian club will look to sign Lazio's Keita Balde as a replacement, and have already made progress on that purchase.
United manager Jose Mourinho sees Perisic as a key signing for the completion of his side, both for his defensive work and different attacking contribution in terms of crosses - a quality United have lacked.
United remain interested in a defensive midfielder with Mourinho informing the club to do a deal for either Chelsea's Nemanja Matic or Eric Dier of Tottenham.
Mourinho had hoped to get the majority of his business before the club's pre-season tour of the United States but hitherto, ahead of Perisic's arrival, has only got deals for Victor Lindelof and Romelu Lukaku over the line.
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