Mr Koum, who sold WhatsApp to Facebook for $19 billion in 2014, has offloaded around 43 million Facebook shares over the past year.
The bulk of the shares were sold in more than 120 transactions since April 1 last year, bringing him more than $3.7 billion.
Mr Koum also gifted around 12.6 million shares but the filings did not reveal who the lucky recipient, or recipients were.
The combined moves have taken Mr Koum's ownership of Facebook's Class A common stock from 2.6 percent last year to just 1.2 percent, according to the company's annual proxy statement.
Executives selling stock is common practice, given that shares often represent a large portion of their remuneration but the pace of Mr Koum's selloff is somewhat unusual.
Facebook founder and CEO Mark Zuckerberg also dumped a lot of his Facebook stock last year. Around $1 billion worth, which was used to fund his philanthropic activities.