Hammond will earn an average of $1.35 million per season ($1.2 million in 2015-16, $1.35 million in 2016-17 and $1.5 million in 2017-18).
The 27-year-old netminder, nicknamed the Hamburglar, carried the Senators on a remarkable run to the 2015 Stanley Cup playoffs after an incredible streak in which he went 20-1-2 in the latter half of the regular season.
Hammond emerged practically out of nowhere to fill the Sens' crease after injuries to Robin Lehner and Craig Anderson. He earned the starting job heading into the playoffs but went 0-2 as the Senators fell to the Montreal Canadiens in the first round.
The Senators announced the news on Twitter.
At the Senators' end-of-season news conference, general manager Bryan Murray said if they were able to re-sign Hammond, they would trade Anderson or Lehner.
ESPN.com's Pierre LeBrun contributed to this report.