The 32-year-old Frenchman arrived at Pride Park in January as a free agent, signing a deal until the end of the season with the Barclays Premier League basement club.
Derby manager Paul Jewell told his club's website, dcfc.co.uk: "It didn't quite work out for Laurent here, but we wish him well in the future."
"He's a tremendous player with a lot of talent, and we expect him to come in and make an impact with our club straightaway.
"He's played at every level and is a true professional in every aspect."
Robert's biggest career move came when he signed for Newcastle in 2001 and played under current Toronto coach John Carver.
"I've spent a lot of time with Laurent and know a lot about his game," said Carver.
"He'll be a big asset to the team."