The acqusition is expected to be immediately accretive and strengthen Allergan's portfolio of medical aesthetics with the addition of Zeltiq's CoolSculpting system.
The US Food and Drug Administration (FDA) cleared the CoolSculpting system to affect appearance through lipolysis or reduction of unwanted fat by utilising a patented cooling technology.
Based on the scientific principle that fat cells are sensitive to cold compared to overlying skin and surrounding tissues, the system is claimed to gently cool targeted fat cells in the body to trigger a natural, controlled removal of fat cells without affecting surrounding tissue.
Allergan chairman and chief executive officer Brent Saunders said: "The acquisition of Zeltiq is highly complementary and strategic to Allergan.
"By adding the best-in-class body contouring CoolSculpting System to our best-in-class facial aesthetics, plastic surgery and regenerative medicine offerings we are creating a world-class aesthetics business.
"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, putting Allergan in a unique position to provide expanded customer service, and help meet the needs of patients."
Subject to customary adjustments and approval by the shareholders of Zeltiq, the transaction is expected to be complete by the second half of this year.
It is reported that millions of treatments have been performed by using more than 5,700 CoolSculpting systems in more than 80 countries.