The 30-year-old described the move as "a no-brainer" but acknowledged the scale of the challenge awaiting Hull as they prepare for a return to the Premier League.
"I'm at an age now where I feel like I am an experienced head to pass on previous experience of the Premier League to players who have not been in this situation," Targett said.
"I'm hoping I'll be a huge help in the dressing room."
Targett has previously represented Southampton, Aston Villa and Newcastle in the Premier League, and spent last season on loan in the Championship with Middlesbrough, where he started in their play-off final defeat to Hull. He explained how the move came together, revealing his agent's call arrived during England's game on Saturday night.
"The next minute, I was on a phone call with the owner. He is very invested in the football club and speaks very passionately, so it didn't take much convincing to join."
Looking ahead to life back in the top flight, Targett drew confidence from the recent example of other promoted sides.
"It's going to be a massive challenge, but we can take huge confidence from what the likes of Sunderland and Leeds did last season."
Targett made 46 appearances for Middlesbrough last season, scoring four goals, and his experience of both promotion football and the Premier League is expected to prove valuable for a Hull squad adjusting to the step up in quality. His arrival follows the earlier additions of goalkeeper Jack Butland from Rangers and midfielder Oscar Zambrano from Maribor, as the club continues to build a squad capable of competing following their return to the top flight after nine years away.
Targett's route to Hull City comes after he left Newcastle at the end of his contract without adding to his six senior appearances for the Magpies, having struggled for game time following his move from Aston Villa.
His most productive spell in recent seasons came at Villa Park, where he established himself as a regular Premier League left-back before a loan move to Middlesbrough last term reignited his career, culminating in the play-off final defeat to the very club he has now joined. That familiarity with Hull's squad and system, built up over 90 minutes on the losing side in May, is seen as one of several factors that made the move an easy decision for both parties.