The Marylebone Cricket Club (MCC) has been granted permission by Westminster City Council to replace the Warner Stand at the London ground.
The MCC said the new structure, which includes a 135-seat restaurant with views of the ground, will improve sight-lines and accessibility.
Work is set to begin on the Â£21m project at the end of the 2015 season.
The redevelopment must first be approved by the club's membership, with the committee set to seek approval at a special general meeting in the summer of 2015.
The current Warner Stand was built in 1958 and its replacement is the first phase of development in the 15-year Masterplan for Lord's, which was unveiled last May.
MCC chief executive Derek Brewer said the club "wants Lord's to be the world's finest cricket ground and this new stand combines the best in architecture with world-class facilities to help achieve that".
"Lord's celebrates its 200th birthday this year and we have a duty to ensure any changes made to the ground will stand the test of time and bring long-term benefits."
He added the MCC, who remain the guardians of the laws and spirit of cricket, will continue to consult with local residents in St John's Wood about the ground's redevelopment.

The defender, 27, was carried off after he was injured in an 85th-minute collision with opponent Theo Hernandez.
Barcelona said on Saturday evening that Vidal, signed from Sevilla in 2015, would be out of action for five months.
"Aleix, you'll be back stronger - get well soon," wrote team-mate Andre Gomes on Twitter.
Vidal had recently established himself as a regular in Luis Enrique's side, scoring in league victories over Las Palmas and Athletic Bilbao since the turn of the year.
After suffering his injury, he was taken to hospital in the Basque city of Vitoria-Gasteiz, where Alaves are based, for an operation to reduce the swelling on his ankle.
His was one of two serious injuries sustained in La Liga matches on Saturday; Osasuna defender Tano Bonnin broke his leg during the first half of their 3-1 defeat at home by Real Madrid.
Plans to redevelop a stand at Lord's, the home of cricket, have been given the go-ahead.
[NEXT_CONCEPT]
Barcelona full-back Aleix Vidal will miss the rest of the season after dislocating his right ankle during Saturday's 6-0 La Liga win at Alaves.