The move is the latest in a string of takeovers in Italy by cash-rich Chinese buyers.
The takeover gives ChemChina access to technology to make premium tyres and gives Pirelli greater access to the Chinese market.
Pirelli shares were 2.56% higher at €15.62 on Monday on the news.
ChemChina's tyre making unit, China National Tire & Rubber, is to buy the 26.2% stake in Pirelli owned by Italian investment firm Camfin. It will then launch an offer for the remaining shares.
Camfin said the bid would be launched by a consortium controlled by ChemChina but also part-owned by Camfin investors, who include Pirelli boss Marco Tronchetti Provera, Italian banks UniCredit and Intesa Sanpaolo, and Russia's Rosneft.
The offer will be launched at €15 per share, valuing the group at €7.1bn excluding net debt of almost €1bn.
Following reports of the deal on Friday, shares in Milan-listed Pirelli hit a 25-year high, closing at  €15.23.
Current Pirelli chief executive Tronchetti Provera, who started working for tyre maker in 1986 after marrying a member of the Italian family that founded the firm, will remain in his post.
Previous Chinese acquisitions in Italy include stakes in power grid firms Terna and Snam, turbine maker Ansaldo and luxury yacht maker Ferretti.
Chinese state-owned China National Chemical (ChemChina) is to buy Italian tyre maker Pirelli in a deal which values the firm at €7.1bn (£5.1bn).