The deal, revealed by Building two weeks ago, was announced to the stock market last Tuesday.
Rok chief executive Garvis Snook said Llewellyn would be restructured to fit the enlarged Exeter group. He admitted that the restructuring, which is expected to cost £1.5m over two years, would lead to job losses.
Snook added that turning around the Eastbourne firm, which posted a £2.8m loss in the six months to March, would be a challenge. He said: "It's a big job – the contracting business hasn't been making money for a long time.
But it's also an enormous opportunity."
Snook said he intended to keep the Llewellyn brand and added that the acquisition was part of Rok's plan to create a national group using regional businesses.
The deal, which will lift Rok's turnover to more than £300m, is made up of £2m of Rok shares and £14.25m in cash.
Rok is raising £6m through a placement of shares and will use bank loans to make up the balance. The firm also plans to raise up to £3m by selling some of Llewellyn's non-core businesses.
Llewellyn operates throughout the South-east and employs more than 650 staff. It concentrates on the retail, leisure, office, PFI and housing sectors.
Rok has itself been restructured since Snook took over in 2000. He oversaw its transformation from a small, regional contractor into a group with property and maintenance arms. This involved making about 120 staff redundant.
Rok's pre-tax profit for the six months to 30 June was £1.77m, a rise of 48% from £1.2m for the same period last year. Turnover increased £11.3m to £66.8m.