The Serie A club rejected that offer and Sky in Italy understands new manager Luciano Spalletti would be keen to keep Perisic at the San Siro if their £44m valuation is not met.
And after meeting with the club's owners in China, he has now put pen to paper on a contract, with Inter confirming the news on their official Twitter account.
Inter announced the news on Friday, adding that Spalletti will be unveiled as their new boss on Wednesday.
Chinese electronics retailer Suning Commerce Group Co Ltd bought almost 70 per cent of Inter for €270 million (RM1.29 billion) in June, less than three years after the club had been sold to a consortium led by Indonesian business tycoon Erick Thohir. "He will take his first training session with the team on Monday 3 July", the club stated on its website.
"Luciano Spalletti has been involved in more Serie A matches than any other coach now employed in Serie A - 406 and counting".
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"Best of luck in the new job, Luciano!"
The 58-year-old guided Roma to second place in Serie A with an impressive 87-point haul last season but off-field issues hastened his exit from the Stadio Olimpico last month.
Youth coach Stefano Vecchi coached Inter for one match after De Boer's firing, and then again for the final three games of the Serie A season after Pioli was sacked.
Spalletti's appointment had been widely expected given his relationship with Inter sporting director Walter Sabatini, who also recently joined from Roma.
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