Atkins, who started on Tuesday, will handle the day-to-day running of the group, freeing up chief executive Ross Taylor to concentrate on strategy.
Formerly head of Bovis Lend Lease's mid-Atlantic region, Atkins joined the firm in 1980. He worked in North and South Carolina, Maryland, Virginia and Colombia.
Taylor said his role would open out as a result of Atkins' appointment.
He said: "I shall be working on our growth strategies, key customers, our people and the vision and values that define our business culture." Ring replaces former financial head John Nesbitt, who is moving to a financial role at parent firm Lend Lease in Australia.
Ring was formerly European commercial director at Bovis and developed the firm's PFI portfolio.
The appointments follow a boardroom reshuffle at the group last year.
The shake-up saw Taylor take up top spot as chief executive and John Spanswick become European managing director.
In addition to these changes, former chairman Frank Lampl was made president and former chief executive Luther Cochrane became group chairman.
The new appointments will build on Bovis' expansion into Europe. It has already acquired German project management firm IRW and formed a joint venture with the property arm of Italian tyre manufacturer Pirelli.
Bovis Lend Lease posted an operating profit of £14.9m for the six months to 31 December 2000.