The club says the extra 2,500 seats will help a growing demand for tickets and will be granted upon a safety certificate application being completed.
The expansion will give put West Ham above Arsenal's Emirates Stadium (capacity: 60,260) in the Premier League's stadium attendance charts.
"The application to increase the matchday capacity will give an even greater number of our fans the opportunity to watch our exciting team in action in person," West Ham vice-chairman Karren Brady said.
"Since the regular return of supporters this year, we have seen a terrific response with every Premier League fixture so far this season sold out, and we thank them for their continued fantastic backing including breaking attendance records as part of regular capacity crowds at London Stadium.
"This is another great sign of progression during a hugely positive time for the club."
West Ham moved from Upton Park in 2016 to the showpiece venue from the 2012 Olympics.
After some initial teething problems the stadium now plays host to David Moyes' side in European action as well as domestic competitions.
"Everyone here is doing everything we can to grow and develop this football club, on and off the pitch, for the benefit of our supporters, and we all feel that things are moving in the right direction," Moyes said.
"The supporters being back has been fantastic and the atmosphere they have created, with 60,000 in the stadium, has been right up there every game.
"Having more fans in here cheering the team on will make it even better for us all and we are really looking forward to welcoming more of our young supporters and families to London Stadium."
The long-term plans are to increase capacity as high as 67,000 in the coming years, which would put West Ham second in the Premier League attendance charts above the Tottenham Hotspur Stadium.