Defender Tomori broke into the Chelsea team last season under Frank Lampard but has been out of favour this season with Kurt Zouma and summer signing Thiago Silva above him in the pecking order, while Antonio Rudiger has also been given starting minutes in recent weeks.
The 23-year-old has signed a loan deal until the end of the season with an option to buy for around £25million, should Milan be impressed with his contribution at the San Siro. The Italian club had been monitoring Tomori for some time and director Paolo Maldini this week described him as “the perfect fit".
Meanwhile, after Arsenal manager Mikel Arteta survived a difficult run of form earlier this season and looks to have turned the club around, the Spaniard said his Chelsea counterpart Frank Lampard should also be given time to get them back on track.
Lampard is under huge pressure at Chelsea after Tuesday's 2-0 loss to Leicester City saw them slip to eighth. They have now lost five of their last eight in the Premier League.
"I have known Frank for a few years and I spent some time with him and I would like the club to support him and give him a chance," Arteta, who like Lampard captained the club he now manages, told British media.
"He has huge experience as a player, he is an icon over there. You need time, and something we have not had in this calendar year is time to work on anything."
Arsenal's form nosedived during November and December and Arteta only managed to turn the tide with a win over Chelsea on 26 December. They are now unbeaten in six games in all competitions.
"I can only talk about what I have experienced ... it was full support in difficult times," said Arteta, whose side face Southampton in the FA Cup fourth round on Saturday.
"Fortunately if they see what you are trying to do is going to have rewards in the future, and they are a little bit patient, most of the time it pays off."
Additional reporting by PA