Bayer said in a statement that the sale, aimed at sharpening the company's focus on life sciences, was expected to be concluded in mid-2020 pending anti-trust clearance.
Bayer's Animal Health business is a global leader in the segment with sales of $1.8 billion last year. The deal will create the number two in the sector.
The transaction will consist of $5.3 billion in cash and $2.3 billion in Elanco stock, Bayer said.
It pledged that under the sale, "all Bayer Animal Health employees will have at least one year of employment protection against unilateral termination with similar and no less favourable benefits in the aggregate".
As it struggles with ebbing revenues and profits, Bayer is selling off several divisions including chunks of its over-the-counter medicines division, known as Consumer Health.
The unit includes household-name brands like painkiller Aspirin and indigestion treatment Alka-Seltzer.
Earlier this month Bayer and its former subsidiary Lanxess announced the sale of their chemicals firm Currenta to Macquarie Infrastructure and Real Assets in Australia for 3.5 billion euros ($3.9 billion).
After taking over US seeds and pesticides giant Monsanto for $63 billion last year, the Leverkusen-based group is reorganising itself around its core businesses and biggest earners in agrichemicals and prescription pharmaceuticals.
Meanwhile it is busy battling thousands of US lawsuits over flagship Monsanto herbicides containing chemical glyphosate, which plaintiffs argue caused them to develop cancer after years of use.
Bayer shares had gained around 0.26 percent at 66.47 euros around 12:00 pm (1000 GMT) in Frankfurt, in line with the DAX index of blue-chip German stocks.