The Senators didn't say how much they will be paying Anderson through the 2014-15 season, but the Ottawa Citizen reported the deal is worth $12.75 million.
Ottawa swapped goalie Brian Elliott with Colorado to get Anderson, who has gone 6-4-0 with a 2.11 goals-against average in 11 games for the Senators.
"Goaltending is and will be one of the important building blocks consistent with our plan to improve the team moving forward," Senators General Manager Bryan Murray said. "Craig has provided a level of confidence to this team and this organization that was lacking early in the season, and we feel he is the type of person and player that will be a big part of our organization's future success."
While missing parts of the season, Anderson, 29, was 13-15-3 with a 3.28 GAA in 33 games with Colorado.
In 224 games since the 2002-03 season, Anderson has a 93-87-19 mark with two ties, a 2.81 GAA and 15 shutouts with Chicago, Carolina, Colorado and the Senators.
Ottawa is in last place in the Northeast Division and in the Eastern Conference with a 27-36-9 record.