The England defender left White Hart Lane after nine-and-a-half years' service to pen a three-year-deal at the KC Stadium.
After comfortably surviving in the top flight and reaching the FA Cup last season, Hull had been expected to push into mid-table, though that has not materialised.
Four points from a trip to Manchester City and home clash with Aston Villa have given them some rare upward momentum though, and Dawson hopes Saturday's visit of QPR to the KC can provide another success.
"It has been a different experience being down near the bottom of the division, but I'm here to fight for the team," Dawson told the club's official website.
"When I came here, I believed the squad that we had would be fighting in the middle of the table rather than against relegation.
"But as long as we stick together and fight for one another I believe this squad is good enough to climb this table.
"It's no good talking about it though. We have to physically do it and get enough points on the board to get us to safety."
