Harper will provide competition for Scottish keeper Allan McGregor, signed from Besiktas earlier this month, with Bosnian stopper Eldin Jakupovic another option for Tigers boss Steve Bruce.
"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 3-1 friendly win at North Ferriby on Monday night.
"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."