Dublin-based Allergan will pay $56.50 per Zeltiq share, a 14.4% premium to the group’s closing price on Friday.
The acquisition will give Allergan access to Zeliq’s body contouring technology, CoolSculpting System, which reduces stubborn fat cells that may not respond to diet or exercise.
The technology will compliment Allergan’s treatment, Kybella, which is used to reduce fat under the chin.
Allergan said body contouring presents a $4bn market opportunity worldwide and the purchase of Zeltiq will be immediately earnings accretive.
"With CoolSculpting, our offerings to plastic surgeons, dermatologists and aesthetic practitioners will now extend to three of the largest and fastest-growing segments of their practices," chairman and chief executive Brent Saunders said.
The acquisition is subject to shareholder approval.
Since its $160bn merger with Pfizer collapsed in April, Allergan has been involved in a batch of deals including the acquisition of Acelity's LifeCell.
Allergan announced it was buying LifeCell, which produces products for breast reconstruction and soft tissue repair, in December and it is expected to boost the company’s earnings in coming years.