The Edinburgh-based investor said the deal marked further progress towards its goal of becoming an “integrated IT services and cloud provider”.
The deal comes hot on the heels of another acquisition last month where Aim-quoted Castle Street struck a £34.8m deal to buy IT and cloud services firm Selection Services Investments.
Castle Street chief executive Andy Ross said: “C4L has a high quality, next generation infrastructure which has been well invested. Allied to a successful business with high levels of recurring revenue it offers strong growth opportunities.
The Bournemouth-based company was founded in 2000 and today's serves more than 800 customers.
C4L chairman and founder Matt Hawkins will join the Castle Street board as chief technology officer. Simon Mewett will also become CEO.
In the last set of filed accounts at Companies House for the fiscal year ended 31 October 2014, C4L reported an operating profit of £239,314, down 53 per cent year-on-year which was blamed on a delayed network upgrade.
Analyst Megabuyte said the buy makes sense, “with the combination of managed services and networks meeting the increasing trend among UK mid-market businesses to buy properly converged services from fewer suppliers in an increasing hybrid cloud/ IT world”.