Harper ended his 20-year association with Newcastle United earlier this summer and has joined Hull to provide competition for Allan McGregor and Eldin Jakupovic.
The 38-year-old is happy to lend his experience to the Tigers' bid to stay in the Premier League and he is looking forward to a fresh start.
"I came down this morning and had a very thorough medical, and then trained with them all this afternoon," Harper told Sky Sports News after the friendly win at North Ferriby.
"I was told they're a good bunch of lads and paths have crossed with the gaffer a few times as well.
"It was great to see them play and 3-5-2, you don't see that very often, but it worked and they passed the ball well.
"I'm looking forward to it. It's a new challenge, a new chapter. It won't be as long as the last chapter, but I'm looking forward to it."
Keen to challenge
Though Harper's experience will be a boost on Hull's return to the top flight, he is still keen to challenge for a starting spot in Steve Bruce's side.
He added: "I've said to Allan and Eldin, the other goalies, I'm here and we're all in this together.
"It's going to be a long year in this league, but we're going to have a right good go, and anything you want to ask me, fire away.
"I've probably been there and seen it in this league, and certainly after 20 years at Newcastle, you've seen quite a lot as well.
"I'm here to be competitive and make it hard for the manager, and give him a selection dilemma when it comes to the goalkeeping department."