The veteran stopper was released by Newcastle United at the end of last season after 20 years at the club, but joined the Tigers on a free transfer on Monday.
Harper, who will provide competition for Allan McGregor and Eldin Jakupovic, cannot wait to get started with his new employers.
"I came down this morning and had a very thorough medical, and then trained with them all this afternoon," Harper told Sky Sports News. "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."
Hull's next match is a friendly against Sheffield Wednesday on Saturday.