The extension will pay Burfict $7.6 million this year, a source told Schefter.
Burfict was not at Bengals practice Wednesday due to what defensive coordinator Paul Guenther called a "stomach bug."
The linebacker, heralded as the unquestioned leader of the Bengals' defense -- a unit that finished 2013 ranked third overall -- was due a contract extension with his rookie deal expiring at the end of this season.
Signed as an undrafted free agent out of Arizona State, Burfict was set to make about $570,000 this season.
As part of his Pro Bowl second season, Burfict led the league in tackles last season with 171. He becomes the second Bengal signed to a contract extension this month, joining quarterback Andy Dalton, who agreed to a six-year extension that will pay him up to $115 million.
ESPN.com Bengals reporter Coley Harvey contributed to this report.