April 18 (Reuters) - Concord Chorus, a music and theatrical rights firm, has agreed to acquire British music investor Hipgnosis Songs Fund for $1.40 billion, the companies said on Thursday.

Shareholders of Hipgnosis Songs will get $1.16 apiece in cash, representing a premium of about 32% based on current exchange rates, and the company's board plans to unanimously back the deal.

Concord said its financing partner Apollo Global Management will help finance the deal.

Concord is indirectly controlled by Alchemy Copyrights, which acquired music copyright-focussed investment firm Round Hill Music Royalty Fund last year.

($1 = 0.8016 pounds)

(Reporting by Yadarisa Shabong in Bengaluru; Editing by Sherry Jacob-Phillips)