Baird, 33, has joined the West London outfit on an emergency loan deal until the end of the campaign.
The Northern Ireland international, capable of playing in defence or midfield, has made 16 appearances for Derby this season after joining from West Bromwich Albion last summer.
Head Coach Darren Wassall explained: “Chris obviously has a very big summer ahead of him with Northern Ireland at the European Championships and as a club, we wanted to give him the best chance of doing well in such a massive international competition.
“Chris has been a complete professional since I became Head Coach 10 days ago. He has supported me brilliantly in training, on and off the field, and last night we wished each other all the best when we spoke.”
Baird spent six years with Fulham between July 2007 and July 2013, making 165 appearances in total for the Cottagers.
Fulham are currently 19th in the Championship and are six points above the relegation zone.