The deal will combine Dentsply's single-use dental supplies, such as paste and sealants, with Sirona's advanced technology equipment, such as imaging systems and instruments.
"There is a convergence now of consumables and technologies in the dental space. With the two of them together, Dentsply and Sirona can become even more relevant to dentists across their product needs," said Jon Santemma, global head of healthcare investment banking at Jefferies LLC, which advised Sirona on the deal.
Sirona shareholders will receive 1.8142 shares of Dentsply for each share held. The offer works out to $98.60 per share and represents a 0.7 percent discount to Sirona's Tuesday close.
Sirona's shares rose about 2.5 percent to $101.75 after the bell, while Dentsply stock was up about 2 percent at $55.41.
Dentsply shareholders will own 58 percent and Sirona shareholders 42 percent of the combined company after the deal closes, expected in the first quarter of 2016.
The deal value was calculated based on 56.4mn Sirona diluted shares outstanding as of June 30.
Sirona's Chief Executive Officer Jeffrey Slovin will serve as the combined company's CEO, while Dentsply's CEO Bret Wise will be the executive chairman.
The new company, to be called Dentsply Sirona, will have net revenue of about $3.8bn on a pro forma basis for the past 12 months, the companies said.
The stock issuance in the merger is expected to be tax-free to shareholders of both companies.