Terms were not disclosed but sources told ESPN's Adam Schefter that the contract is worth $68 million.
The Falcons had until 4 p.m. ET to agree to the deal with Jarrett, who initially received the $15.209 million franchise tag. Jarrett had signed the tag, which was a precursor to the long-term deal, in April.
"As we have said since the end of the season, getting a deal done with Grady has been a priority and we are pleased to have accomplished that today," Falcons general manager Thomas Dimitroff said in a statement.