The deal, worth around £7.9m is made up of £5m upfront followed by £2.9m in performance milestones over the next year, is expected to lift AdEPT's earnings by 10 per cent.
Shares were lifted as much as five per cent during trading, before easing to more than a two per cent rise later on in the day.
AdEPT said the acquisition of Shift was complementary to the business, which provides IT management, communications, connectivity and voice solutions services to clients.
Surrey based Shift offers telecoms and IT solutions to businesses, with a focus on London and the south east. It will retain its management team after the completion of the deal.
Ian Fishwick, chief executive of AdEPT, said:
We are delighted to have acquired such a high quality, well-run and profitable business with a strong management team. Shift F7 is an excellent fit because it enhances our market position in IT, particularly in London. Shift F7 complements our acquisition of OurIT in February 2017 which is also focused on London and South East commercial customers.
After the Shift F7 acquisition, more than 70 per cent of AdEPT revenue will be generated from managed services including IT support, unified communications and data networks. The Acquisition is expected to be earnings enhancing from completion.