Skanska was selected for the £500m Lime Street Tower, otherwise known as the Scalpel, back in July 2013, but has only now formally signed the £198m construction contract with client WRBC Development UK.
The building at 52 Lime Street will be 190 metres high, making it 10 metres taller than the neighbouring Gherkin building at 30 St Mary Axe.
Designed by architect Kohn Pederson Fox, it will provide 37,000 square metres of office accommodation over 35 office floors.
Lime Street Tower will be the European headquarters of US insurance company WR Berkley Corporation, which will occupy about 20% of it.
Planning permission was granted early last year. Work finally starts this month and is scheduled to finish in 2017.
Skanska is responsible for the construction, mechanical and electrical engineering and installation of services within this new development.
The plans for the public space created by the development include re-establishing Lime Street Square, which was destroyed in the blitz in 1941.