The all-cash deal values Pall at $127.20 per share, a 28% premium above the closing price on May 11, the last day prior to media stories on the possible transaction.
Danaher, which provides industrial goods and services in dental, petroleum and other sectors, said Pall's sophisticated filtration products would boost its water business.
"Pall will provide us a leading business with significant runway for expansion and strengthens our life sciences position in the strategically attractive, high-growth biopharmaceutical market," said Danaher chief executive Thomas Joyce.
Pall will operate as a subsidiary of Danaher and will keep its brand.
Pall had revenues of $2.8 billion in 2014, while Danaher had revenues of $19.9 billion.
Danaher also announced it would split into two independent publicly traded companies.
The larger "science and technology" company, which will include Pall, comprises life sciences, water quality and dental segments, while the smaller "diversified industrial growth" company includes brands in automation and sensors.
"Each company will be more focused with access to the capital necessary to pursue organic and inorganic growth opportunities," Joyce said.
Copyright Agence France-Presse, 2015