Revlon hopes the acquisition will expand its global footprint.
Elizabeth Arden, famous for its Eight Hour Cream and Taylor Swift and Justin Bieber fragrances, has a strong presence in the Asia-Pacific region.
Revlon's boss described the firm as "one of the last independent, iconic brands in the cosmetics industry."
Canadian-born entrepreneur Elizabeth Arden founded the company in New York City in 1910. She is credited with inventing the makeover and was the first to introduce eye make-up to American women, according to the company's website.
Revlon hopes to benefit from Elizabeth Arden's strength in prestige skincare and fragrances, which would complement Revlon's strength in lipstick and nail varnish, hair care and men's grooming.
It typically distributes its products through mass retailers and beauty salons.
Elizabeth Arden, on the other hand, has a strong presence in high-end and travel retail channels but has been struggling in recent years.
Both companies sell their products in more than 120 countries, and when combined are expected to have sales of around $3bn.
Revlon said it would pay $14 per share for Elizabeth Arden, which represents a 50% premium on the company's share price just before the deal was announced.
"This acquisition is strategically and financially compelling," Revlon's chief executive Fabian Garcia said in a statement.
"Combining our brands, talent, and global distribution will give our company a significant presence in all major channels and categories, while accelerating sales growth in existing and new geographic regions."
Elizabeth Arden has struggled in recent years as sales of celebrity fragrances have declined and in 2014 it announced a restructuring programme to improve profitability.
It reported a net loss of $28.4m in the quarter ending March 31, but said restructuring plans were on track.
Revlon expects the tie-up, which should be completed by the end of this year, to result in savings of up to $140m.
Revlon was founded during the Great Depression in 1932, when it introduced nail enamel available in multiple colours. It later added lipstick and other products. The company reported a profit of $11m in the first quarter of 2016, following a $900,000 loss in the same quarter last year.
Revlon, known for its make-up and hair care products, has agreed to buy Elizabeth Arden in a $870m (Â£609m) deal.