The Italian architect is working alongside US giant SOM to deliver the scheme, which involves razing masonry-clad factories - dating from up to a century ago - whose owners are refusing to sell.
Speaking to New York's Architectural Record, Piano said: 'Cities are bound to change - you have to accept it. You can't embalm a city.'
Columbia's plans to build a new campus as large as its original campus, 10 blocks south, has led to a stinging backlash from local residents, who believe their neighbourhood is slowly being eroded.
Piano, however, is defiant: 'We saved buildings that will give a good sense of the history of this neighbourhood. It's a mix of the past but, at the same time, the courage to go ahead and change.'