It is set to be built after the London Legacy Development Corporation's planning committee voted six to four in favour of the proposal.
It made the decision despite 852 objections submitted in opposition to the project. In total, 355 responses were received supporting the proposal.
"The applications have been subject to robust review and a detailed officer report," said an LLDC spokesperson.
"Following careful consideration, the independent Planning Decisions Committee has approved granting full planning permission for the MSG Sphere, subject to conditions," the spokesperson added.
Following the agreement of Section 106 planning obligations, the application will be referred to the London mayor's office for final approval.
Designed by stadium-specialist Populous, the venue will have a capacity of 21,500 with 17,566 seated.
It will be built on a triangular site, which is surrounded on all sides by railway lines, alongside the Westfield Stratford City shopping centre.
The main auditorium would be placed within the 90-metre-high sphere along with restaurants, cafes and a members' club. Within the sphere, the interior surface will be covered in an "immersive LED surface" that could be utilised for esports.
"MSG Sphere London is a natural fit for events such as esports, where audiences will be able to participate in the competition and interact with each other," said a statement from MSG when the project was first revealed.
"It represents an important milestone in the company's vision to redefine live entertainment through iconic venues that will feature game-changing technologies and pioneer the next generation of transformative, immersive experiences."
The sphere would rise from a podium building that will contain shops and a nightclub.
Externally it will be covered in LED screens that will be used for promoting upcoming events or for advertising.
The venue is one of a pair of sphere-shaped arenas designed by Populous that were first revealed in 2018. Its almost-identical sister venue is currently under construction in Las Vegas and scheduled to be complete next year.
The building will be the latest in a series of spherical buildings. We recently rounded up nine globe-shaped buildings from around the world.
The imagery is courtesy of Madison Square Garden Company.
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