The fund controlled by billionaire Leon Black will pay $54 per share for CEC, a premium of 11.5 percent to the stock's Wednesday closing.
The deal represents a premium of about 25 percent to CEC's closing share price on Jan. 7, when first reports of a possible deal emerged, Apollo said.
Including debt, Apollo valued the deal at $1.30 billion.
Separately, CEC said it had adopted a poison pill with a 10 percent trigger.
(Read more: Chuck E Cheese parent CEC explores sale: Sources)
However, the company said this would not prevent it from scouting for a superior offer under the terms of the deal agreed with Apollo.
CEC and its franchisees operate 567 entertainment-focused Chuck E Cheese restaurants in 47 U.S. states. The restaurants offer musical and robotic entertainment, games, rides, play areas and food such as pizza and sandwiches.
Reuters reported last week that CEC was working with Goldman Sachs Inc and was speaking with interested buyers over the last several months.