According to Official Guinness Records,
The most pass completions in an NFL career by a quarterback is 6,326, and was achieved by Drew Brees (USA) playing for the San Diego Chargers and the New Orleans Saints, from 4 November 2001 to 23 September 2018. Brees beat the previous record, held by Brett Favre, in a 43-37 victory over the Atlanta Falcons.
For a complete list of 2018 records, please visit 2018 Guinness Records in United States.