Baird played 16 times for the Rams after arriving on a free transfer last summer, but was left out of Wassall's squad entirely for Saturday's 1-0 defeat to Preston North End.
The Northern Ireland international's last appearance ironically came in a 1-1 draw against Fulham 12 days ago, in what proved to be Paul Clement's final game in charge.
And former academy coach Wassall, who was sworn in immediately after, described Baird as "a complete professional" after the 33-year-old agreed a three-month stay at Craven Cottage.
"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," he told the Derby Telegraph.
"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 we wished each other all the best when we spoke."
Baird, who began his career at Southampton, spent six years at Fulham between 2007 and 2013, before short spells at Reading, Burnley and West Bromwich Albion.
The 74-capped international played all 120 minutes of the Cottagers' Europa League final defeat to Atletico Madrid six years ago.