The capacity of Lord's will increase to 31,000 after planning permission was granted for work on the Edrich and Compton stands.
Work will begin in August and the seating should be ready for the 2020 season at a cost of £50million, with full completion - including catering facilities - to be ready for 2021.
The stands, which flank the media centre at the Nursery End, will become three tiers and will offer "vastly improved sightlines for the seats in the lower levels".
There will be 2,500 extra seats, taking the capacity to above 30,000, after planning permission was granted by Westminster City Council.
Marylebone Cricket Club chief executive and secretary Guy Lavender said: "MCC is delighted to receive planning permission for the redevelopment of the Compton and Edrich Stands.
"We are excited to be commencing another transformational development at Lord's, and by raising the capacity to 31,000 we will be able to welcome more spectators to enjoy matches at the largest cricket ground in the country, here at the Home of Cricket.
"The redevelopment will be an outstanding addition delivering world-class facilities, ensuring that Lord's remains the finest ground in the world to watch and play cricket."