The England international arrived in a deal worth €40m plus €5m bonuses, while Chelsea retain a buy-back clause set at €80m.
He landed at Ciampino Airport in Rome this afternoon accompanied by director Tiago Pinto, then was whisked off to the Trigoria training ground for a brief meeting with Jose Mourinho, going on to the Villa Stuart clinic for his medical.
According to Il Tempo, Abraham was able to by-pass the usual quarantine orders because he is in Italy for work and will remain in the country for under 120 hours.
He must fly back to London in order to complete the paperwork, as following Brexit, an English player no longer qualifies as an EU national.
That means he takes up a precious spot in the squad, which are limited for non-EU players, and has to apply for a different work permit and visa.