Freedom Refreshments is a UK-wide group that employs 160 people. It turned over £16m in 2016.
It is Tayto's third acquisition in England this year after it bought a snack company and a majority stake in a popcorn business.
The company said the deal allowed Tayto to "increase our presence significantly within this sector".
"While we have a strong share of the vending market in Northern Ireland, we only had limited reach into GB," said Paul Allen, the group's chief executive.
Tayto has established a new company, Montagu Group, to hold the vending machine business.
Meanwhile the Tayto Group's annual results for 2016 showed a pre-tax profit of £2.9m on turnover of £163m.
The group employed 1,400 people during the year paying salaries worth £29m.
The best-paid director received renumeration of just under £900,000.
The Tayto Group has been owned by the Hutchinson family since 1956 and is the third-largest snack manufacturer in the UK.
Tandragee-based crisp maker Tayto has bought a Leeds-based vending machine business in a multi-million pound deal.