The undisclosed deal comes just six years after Warren Peel, managing director of Trams, helped lead an MBO with Alex Page to take over the reseller.
"Following our management buyout in 2003, we have been actively seeking to expand the business through new acquisitions," Peel said in a statement.
Rapid, which is based in Fleet with offices in Christchurch and London, built up a strong Apple business in the 1990s and its directors Chris McGregor, Mike Saunders and Paul Hopkins will stay with Trams.
Other Rapid senior managers Patrick Geeson and Garrett Doyle will depart following the deal with the former staying on for six months in a hand-over period.
Trams is aiming to use the acquisition to bolster its technical services division that offers a series of services including installation, warranty support and enhanced product specialisations.