The tower at 100 Leadenhall will reach a height of 263.4 metres making it the third tallest building in the Square Mile.
Plans were submitted by the Hong Kong based Lai Sun Development.
Construction will involve the demolition of existing developments at 100, 106 & 107 Leadenhall Street.
The Cheesegrater 2 will provide over 102,000 sq m of office accommodation, as well as basement showers, cycle parking, ground-floor retail space, two podium terraces and a public viewing gallery on the top two floors which will be served by dedicated lifts.
Chris Hayward, Chairman of the City of London Corporation’s Planning and Transportation Committee, said: “As a leading business district accommodating 483,000 workers every day, it is vital to continue to deliver office space for the significant growth expected with the arrival of the Elizabeth line later this year.
“Leading to a church dating back to the 12th century, this development demonstrates the City’s distinctive ability to house the old and new side by side, while becoming more accessible to creative workers and members of the public.
“More than ever we are seeing businesses make location decisions based on the quality of built environment and public realm that they can offer their employees.
“Today’s committee decision will boost confidence and international talent in the City of London.”