McQuade, who ran Bovis' Manchester office, tendered his resignation over the Christmas period. The move means he can return to Scotland where he previously worked for Bovis on schemes such as the Scottish parliament building.
He is expected to be made regional director for the Miller Group's construction arm in Scotland.
Both firms refused to comment on McQuade's move, but market sources said the main reason was homesickness.
Bovis is currently evaluating who to put in the vacant position
A source close to Bovis, who believed the firm was "very sad" to see McQuade leave, said: "The main reason he is leaving is because he is a family man. McQuade always worked in Scotland up until now and I think he found it difficult to be away from home. Miller has also offered him a very good job."
The Miller Group, the UK's largest privately owned construction group, is expected to announce that 2003 was its 10th successive year of growth in its March results. Turnover is expected to rise 15% on 2002 to £750m.
McQuade's position at Bovis will be temporarily filled by his boss Jason Millett, who took over Bovis' UK operations last year after running the Manchester office. The Bovis source added: "Jason is overseeing that role. Bovis is currently evaluating who to put in that position."
Millett was part of a management shake-up that took place last year at the firm, owned by Australian property giant Lend Lease. In the restructure, Doug Chalmers took over Bovis' defence work and Sergio Casari is now handling the firm's continental European operations. Dennis Bate and former chief operating office Les Chatfield were made special client directors.