Then, on Friday, the team officially signed Winston. The four-year deal is worth $25.35 million, which includes a $16.69 million signing bonus, a source told ESPN's Adam Schefter.
The entire deal is guaranteed under the league's collective bargaining agreement. The contract also contains a fifth-year option that is standard in rookie contracts for first-round picks.
"It shows us that he wants us as much as we wanted him," general manager Jason Licht said.
Licht said the team wanted to get the contract out of the way as soon as possible.
"It's something we wanted to do," Licht said. "And it was something where they had no reluctancy, either. It was fairly smooth. We wanted Jameis to start off on the right foot. There's no reason to punish Jameis. He's going to be treated contractually in terms of money just like any other first overall pick."
Winston is the second quarterback the Bucs have taken with the No. 1 overall pick. Vinny Testaverde was the other in 1987.
"I'm glad we got the contract stuff out of the way," Winston said. "I'm just looking forward to getting with the team. We've got some great teammates and I'm looking forward to working with the coaching staff. Just playing some football. This whole thing has been long for me. But football is what I'm here for and I can't wait."
Winston also said he was surprised by the reaction to a photo he posted on social media Thursday night, showing him with crab legs. While in college at Florida State, Winston was issued a civil citation for shoplifting crab legs.
Winston deleted the picture and said he didn't want to bring negative attention to the Bucs.
"That's the only reason I took the picture down," Winston said. "I didn't want any negative publicity for this day because that took it away from this organization and my family. I never would have expected that."
Asked his reaction, Licht joked: "The world knows -- and Tampa definitely knows -- Jameis loves crab legs."
The Bucs said they don't intend to implement any special measures to ensure Winston avoids trouble off the field.
"We are not bringing anyone in. We don't really need any mentors or anything like that. ... We wouldn't bring anyone in that needs to be babysat or anything like that. That's not the case with Jameis," coach Lovie Smith said.
Licht and Smith both expect veterans in the locker room, as well as others who "really care about our organization" to help Winston get acclimated to being a professional. The young quarterback already has a relationship with Hall of Famer Derrick Brooks and several other former Bucs living in the area.
"Jameis is his own man and Jameis is going to heed the advice of a lot of veterans. I'm sure of it. I've had discussions with him about that," Licht said. "Jameis is going to be his own man. He has to find his own way, just like all of our players."
The Associated Press contributed to this report.