Robson has signed a two-and-a-half-year contract with the option of a further year after the two clubs agreed an undisclosed fee, while both Flood and Killen have joined the Teessiders on free transfers.
Flood's deal extends to June 2011 while Killen's runs until the end of the current season.
Midfielder Robson, 31, who won his seventh senior cap for Scotland in November, has a league title to his name and played Champions League football during his two years at Parkhead.
Republic of Ireland Under-21 international Flood, now 24, began his career at Manchester City and joined Celtic 12 months ago after two seasons on loan at Dundee United, while 28-year-old former City and Oldham striker Killen is a New Zealand international.