Trafford Borough Council has agreed to proposals to fill in the north-west and north-east corners of the ground, lifting the attendance by 7,900, reports the BBC.
The project will cost United £45million but the seats, which will be put in ahead of the 2006/07 season, are expected to earn the club an extra £5million a year.
The increased capacity will mean Old Trafford will be second in size only to the new Wembley (90,000) among soccer stadia in Britain.
Cardiff's Millennium Stadium holds 72,000 while Arsenal's new Ashburton Grove stadium will cater for 60,000 fans.
