The Enquirer exclusively revealed O’Rourke had won the tower – known as the Cheesegrater – earlier this month.
The foundations and preliminary basement works are nearing completion allowing the O’Rourke site team to start in September.
Nigel Webb, Head of Developments at British Land, said: “Laing O’Rourke has an excellent track record of delivering major schemes and we look forward to working with them to deliver The Leadenhall Building, which is set to become a defining City landmark.”
Richard Pilkington, Development Director at Oxford Properties, added: “Laing O’Rourke’s selection as our construction partner is a great milestone for The Leadenhall Building and further underpins our delivery for 2014.”
Roger Robinson, Chief Executive at Laing O’Rourke’s Europe Hub said: “We are delighted to have been awarded this unique project in the City of London.
“It is a complex build programme which will require exceptional engineering capabilities to successfully deliver the landmark scheme that our clients are expecting from us.”
The 47 storey, 736 ft (224m) Leadenhall tower is set to become one of the tallest buildings in the City of London and will combine nearly half an acre of landscaped open space with modern, flexible offices and retail and dining facilities.