Milan coach Massimiliano Allegri said that 29-year-old Mexes - who has been at AS Roma for seven seasons - and Taiwo, 26, who has spent six years with French champions Marseille, would bolster an aging defence.
"We are looking good in terms of defence with the signings of Mexes and Taiwo," said Allegri, who won the title largely relying on veteran players.
Both players came on free transfers, with Mexes set to be paid 4.5 million euros a year according to the Italian media.
Mexes is set to replace Milan legend Alessandro Nesta, 35, in the centre of defence alongside Brazilian Thiago Silva.
Taiwo, who played for Nigeria at last year's World Cup finals, has had a successful spell with Marseille playing a pivotal role in their first league title in 18 years last term and scoring the only goal in their League Cup final victory last month.
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