Allen, whom the Bills traded up to select seventh overall in last month's draft, told reporters he was "shaking" as he met Kelly, who was released from the hospital last month after surgery to remove cancer from his jaw.
The two previously exchanged text messages after Allen was drafted.
"He's the greatest quarterback to play the game, and obviously the greatest quarterback in Buffalo history," Allen said.
"That's where I want to be. That's eventually [the goal of] my career, to be regarded in the city of Buffalo like a Jim Kelly. I think that every quarterback who plays here wants to be in the same sentence as him, just because of what he is and what he holds to the city. For him to come out here is an awesome experience."
Allen and Kelly later entered the locker room for a private conversation.
"He said how to embrace the city of Buffalo," Allen said. "He said a few more things -- I'll keep those behind closed doors -- but I'm still shaking from meeting him. He's a special man."
The Bills traded the No. 12 overall selection and two second-round picks to draft Allen. He became the highest-selected quarterback in Bills history, a distinction previously held by Kelly, the No. 14 overall pick in 1983.
Kelly declined to speak with reporters as he recovers from reconstructive jaw surgery he had in March. The former Bills quarterback, who led the team to four consecutive Super Bowl appearances in the 1990s, walked Friday with the assistance of a cane because his surgery required bone to be taken from his leg.
"For him to come out and show support and show everybody that he's doing well, speaks volumes," Allen said. "That's a tough guy right there to [go through] what he's been through and come out and still be himself.
"He's going to hopefully be a mentor to me, and I'm going to take everything that he says very heavily, just because of what he's done on the field and what he's done for the city of Buffalo. For a quarterback in Buffalo, it's a dream come true to meet a guy like him."