The Detroit native played the first 15 seasons of his NHL career with Nashville before a March 5 trade sent him to the Red Wings. He has 577 points in 977 games.
"David is a good, veteran center, a guy that skates pretty well, gets up and down the ice," Senators general manager Bryan Murray said in a statement.
"We just think the way things shook out for us that having an experienced center that can be a decent faceoff man, be a good defensive player, get points, was very important at this time."
The Senators also re-signed defenseman Eric Gryba to a $2.5 million, two-year deal. Gryba had 11 points in 57 games last season.
Murray said the Senators "continue to talk" about a trade, adding "it's just a matter of if we can get satisfaction both ways."
"We probably will do something else, but I do feel comfortable with the roster," Murray said. "I think that if we have to add we will, but it looks like our young players that have been drafted by the organization and have developed within -- we've got a couple of guys that are ready and if they get a chance I'm sure they'll perform very well."