It means the restaurant chain operator, which also owns the Ask Central and Zizzi brands, will return to private hands less than a year after floating on the Alternative Investment Market.
Cinven said that, as a result of the offer, the proposed dividend of 4.7p per Gondola share announced on 21 September would not be paid.
Taken together with Gondola's debt position as at 2 July, the company has an enterprise value of £900m.
David Ross, chairman of Gondola, said: "After careful consideration and deliberation, the independent directors are unanimous in their recommendation that the shareholders should vote in favour of the acquisition."
The 415p per share offer represents a premium of 29.7% on the price of 320p per share when Gondola came to the market last November.
It also represents a 14.6% premium on the closing price of 362p on 5 September when talks first began.
By Chris Druce