David Beckham backed Guild is issuing new shares priced at 8p in the placing, which values the whole business at £41.2mln.
Blue Star has invested £706,000 in Guild to date and it will retain a 5.95% stake in the business following the float.
"The successful IPO of Guild is an excellent illustration of the potential upside from Blue Star's esports portfolio," said Tony Fabrizi, Blue Star chief executive.
"We believe Guild has an exciting future as a listed company and expect to see our portfolio deliver strong performance as the sector grows in strength."
Guild is one part of Blue Star’s eSports portfolio alongside Dynasty eSports which the company said it has also achieved significant momentum.
Dynasty recently raised £1.75mln which valued Blue Star’s retained 13% stake in the company a £1.3mln, versus an original investment of £428,000.
The company noted that its other eSports investments are being held at a cost of £715,000.
Along with other prior shareholders in Guild, Blue Star has agreed to a 12-month lock-in, preventing it from selling shares.