Lukaku was having a medical at the Serie A club, which is coached by former Chelsea manager Antonio Conte.
The 26-year-old Lukaku was greeted by more than 200 fans when he arrived at Milan’s Malpensa airport at 2 a.m. local time on Thursday morning.
They chanted his name and he smiled and high-fived several fans as he walked past.
Italian media reports Inter will pay United around 65 million euros ($73 million) plus 13 million ($15 million) in add-ons for the Belgium international.
Lukaku, who has been training this week with former club Anderlecht, scored 42 times in 96 matches for United after joining from Everton in 2017.
The transfer window shuts in England at 1600 GMT.
Source: FOX Sport