The Rams agreed a fee in excess of £100,000 before the 24-year-old travelled to the Keepmoat Stadium to agree terms.
Robinson is a graduate of the Watford youth system and made his Premier League debut for the Hornets in 2008.
The pacey forward also enjoyed spells with Huddersfield and Millwall before switching to Pride Park where he scored 18 goals in 67 appearances.
Doncaster manager Paul Dickov was quoted on the club's official Twitter account as saying: "Theo has signed this morning. He offers us pace in abundance; something we've been lacking. He's 24 so he's a really good age for us."