The deal value of $35 per share is at a premium of 14.3% to Zayo's closing price on Tuesday.
Including Zayo's debt of $5.9 billion, the deal is valued at more than $14 billion.
Zayo operates a 209,214 km fiber network in the United States and Europe to connect data centers and serves wireless and landline phone companies. It stands to benefit from rising demand for bandwidth in their markets, driven by cloud computing and streaming.
In March, activist hedge fund Starboard Value has urged Zayo to consider a sale after taking a 4% stake in the company.
Reuters exclusively reported last month about the potential deal.
Boulder, Colorado-based Zayo said in November it would break itself up into two companies. However, in February, the company said it was not in its best interest to pursue a public spinoff as part of its strategic review.
The company had earlier rejected acquisition offers, including from a private equity consortium comprising Blackstone, Stonepeak Infrastructure Partners, KKR, I Squared Capital, Charlesbank Capital Partners, and GTCR.
Zayo will become a private company after the deal closes in the first half of 2020.
Shares of Zayo were up 9% at $33.40 in premarket trading.