The project is expected to generate revenue of $250 million to Leighton over 18 months.
CIMIC executive chairman Marcelino Fernandez Verdes said BG's QGC business, which operates CSG fields in the Bowen-Surat basin and Queensland Curtis LNG export plant at Gladstone, is a good fit for CIMIC and its construction arm, Leighton Contractors.
"QGC's ongoing development of its word-class natural gas reserves is making a major contribution to the Queensland economy and growth of the LNG industry in Australia," he said.
"CIMIC Group and Leighton Contractors bring significant international and Australian experience to the delivery of large scale oil and gas facilities."
Leighton managing director Roman Garrido added that the company's integrated project management engineering and construction capabilities provide clients with a single interface for all civil, structural, mechanical, piping, instrumentation and electrical work for delivering oil and gas facilities.
"We are pleased to continue our valued partnership with QGC and look forward to building on relationships formed with local subcontractors and suppliers," he said.
Construction is expected to begin in late 2015 for completion in 2017.
Some 45 cargoes have been delivered from QCLNG in the nine months to September, with daily production of an average of 98,000boepd, peaking at 118,000boepd.
During the quarter, less than 20% of the gas supplied to QCLNG was from third-party gas contracts, in line with expectations during the ramp-phase.
Train 2 commenced operations in July and commissioning is progressing, ahead of the start of commercial operations.
The BG contract is CIMIC's second significant Surat Basin CSG contract in recent months.
In August the company landed a $300 million, two-year contract to deliver gas field development works in the Surat Basin for Australia Pacific LNG.
Leighton is expected to deliver about 200 wells a year in a series of work packages, in collaboration with its design partner Amec Foster Wheeler to meet the APLNG contract, which had an option for a further two years.
The integrated APLNG project remains on track to reach plateau production in mid-2016.