The initial public offering which will value the firm at £240m, will see its private equity owner Electra Partners sell down its 85% stake to 18%.
The flotation had been cast into doubt following Britain's decision to quit the European Union, but the group revived its plans in August and it will begin trading on 21 September at 160p per share.
Electra, which acquired the firm in 2014 for £91m, will net £153m from the deal.
Hollywood Bowl chief executive Stephen Burns said: "I am delighted with the response we have received from investors toward Hollywood Bowl Group.
“We have achieved a huge amount over the past few years, transforming the business through investment and acquisition."
Burns and other members of the management team will also sell part of their stake in the company but will continue to hold 5.4%.
Last year, the group's 54 centres helped deliver a 9% increase in revenues to £86m while earnings increased 41% to £20.6m.
Bill Priestley, chief investment partner at Electra, said: "This investment is a great example of Electra Partners' investment strategy in action.
“When we first invested two years ago our plan was to accelerate the company's growth and, together with Steve Burns and his team, this is exactly what we have done.
"Altogether these actions have more than doubled the size of the business while transforming it into the UK market leader with multiple levers for future growth."
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