Hill trained at the IMG Madden Football Academy in Bradenton, Fla., where Testaverde works part-time as an instructor. They spent three weeks together, working out three or four days a week -- two generations connected by soaring spirals.
At 48, Testaverde still can sling it, and he enjoyed throwing to Hill, whom he described as a potential star.
"I'm glad the Jets got him," Testaverde said Saturday in a phone interview with ESPNNewYork.com. "New York will love him. I think he has a chance to be a really good, if not great wide receiver."
The Jets think so, too. On Friday night, they traded up four spots in the second round, picking Hill with the 43rd overall choice.
The expectations are getting bigger and bigger for Hill. Joey Clinkscales, the Jets' vice president of college scouting, said Hill compares athletically to Calvin Johnson. Testaverde added two other big names -- Terrell Owens and Keyshawn Johnson.
Not too much pressure on the kid, is there?
"He's built like Terrell Owens," Testaverde said of the 6-4, 215-pound Hill. "He's got that muscular physique. You can just call him a stud. He's fast, quick and has really good hands."
Testaverde, who played for seven teams during a career that spanned two decades, never played with Owens. Asked to compare Hill to a former teammate, he mentioned Johnson.
Johnson and Testaverde played together with the Jets and Dallas Cowboys, forming an explosive tandem in 1998 -- the year the Jets lost a heartbreaker to the Denver Broncos in the AFC Championship Game.
"He reminds me of Keyshawn," Testaverde said. "Except faster."
Hill is fast, all right. At the scouting combine, he blazed the 40-yard dash in 4.31 seconds, soaring up draft boards across the league.
The Jets wanted to add that dimension to their offense, which had zero explosiveness last season.
The Jets also wanted to add size to their receiving corps, replacing Plaxico Burress (6-5). Testaverde believes Hill has the potential to be a force inside the 20.
"He's going to be great in the red zone," he said. "Any time there's a jump ball, he's going to win. He can outjump every corner in the league. He can be a dominant athlete."
The Jets told Hill he will have an opportunity to win the starting job opposite Santonio Holmes, but Hill has a lot of work to do because he came from an offense that completed only 64 passes last season. Georgia Tech employs the triple option, which means Hill did a lot of blocking and not a whole lot of catching.
Hill said it was "a little frustrating," but he vowed to make a successful transition to a pro passing attack.
"They're expecting a lot of things out of me," he said Saturday in a news conference at the Jets' facility. "I'm going to come out here day one and just play and gradually get myself to be a great player."
Hill caught only 28 passes last season (for a 29.3-yard average), but he never thought the lack of productivity would hurt his ability to make the NFL. One of his predecessors at Georgia Tech, Demaryius Thomas, was a first-round pick of the Denver Broncos in 2010. In fact, the Jets studied Thomas' career arc while trying to project Hill's potential.
They gave Hill a first-round grade, wasting little time to trade up for him once the second round began.
"For a team to trade up and get you, it's a great feeling," said Hill, who was projected as a late first-rounder in many mock drafts. "It put a big smile on my face. I'm still smiling on the inside right now."
So is quarterback Mark Sanchez, presumably. He called Hill on Friday night to welcome him to the team, and they already started talking about some of the basics of the playbook.
"He's ready to go, he's excited," Hill said. "I'm excited, too. I'll make sure I get with Tim Tebow, too, because I know they'll be a little bit of change going on there" -- a reference to Tebow in the Wildcat.
The graying gunslinger told Hill to "be a rookie, be a pro, stay in your place." Hill, who knew Testaverde mostly from video games, said it was an "amazing" experience.
"He gave me a lot of tips, how to get in and out of breaks, stuff like that," he said.
Testaverde, who retired after the 2007 season, has gravitated toward the coaching side of football. In fact, he'll be coaching the quarterbacks this fall at his son's high school in the Tampa area.
He said he enjoyed Hill because he was a "good kid and a hard worker. I respect and appreciate that, someone who works at their trade."
No, Testaverde said, the Jets didn't call to pick his brain on Hill. He said not too many people even knew he was working with draft-eligible players at IMG.
Testaverde said Hill's biggest challenge will be learning the intricacies of a pro-style offense. The raw talent is there. Asked if Hill had too much speed on deep balls for his 48-year-old arm, Testaverde laughed.
"I never underthrew him," he said. "After 20 years in this game, I learned that you take a three-step drop instead of a five-step, and get it up early -- especially when you're throwing to a guy that fast."