The ex-Northampton Saints star, who won 61 caps for Scotland, has previously coached at Edinburgh and Lyon.
Smith has also worked as director of rugby at French side USB Bergerac and most recently was head coach for Perigueux.
The 47-year-old will work under director of rugby Clive Griffiths at Doncaster, who lost at home to Cornish Pirates on Saturday in their final game of the Championship season.
Knights executive chairman Tony de Mulder said: “We received so many high-quality applications it initially made making a short list extremely difficult.
“When it came to the interviews Tom’s character and knowledge about rugby matters really stood out. I am sure that he will become a worthy successor to Clive Griffiths.”
Unfortunately there was no perfect send-off for Doncaster legends Richard List, Paul Jarvis and Mat Clark.
All three are moving on and hoped to bow out with a win, but Knights were overpowered by their opponents.
Centre Clark only lasted 12 minutes before being led off injured, but he received a standing ovation from the fans as did List, the loosehead prop who has played more than 200 games for the club, when he was replaced in the 46th minute.
Doncaster scored tries via Curtis Wilson, Cameron Cowell and Ben Hunter, Kurt Morath twice converting, but they were no match for Cornish – who scored seven tries through Dan Frost (2), Robin Wedlake, Jack Andrew, Tom Duncan, Alex O’Meara and Maliq Holden – and they finish the season in tenth.