"We went off and we ordered American fast food, paid for by me. Lots of hamburgers, lots of pizza,'' Trump said after returning to the White House from a trip to New Orleans. "I think they'd like it better than anything we could give."
Some players "whooped" when they saw the spread, according a pool report.
"We have some very large people that like eating, so I think we're going to have a little fun," said the president, a fast-food lover himself.
Spokeswoman Sarah Huckabee Sanders said much of the staff that works in the White House residence has been furloughed due to the shutdown, "so the president is personally paying for the event to be catered with some of everyone's favorite fast foods."
An impressive -- and highly unusual for the White House -- smorgasbord greeted the players in the East Room. Silver trays held stacks of wrapped burgers from Wendy's and boxed burgers from McDonald's, including Big Macs.
White House paper cups bearing the presidential seal held the fries.
Pizzas, some topped with olives and tomatoes, also were on the menu. Silver bowls held the condiments and stacks of white china plates sat nearby.
The Clemson team's visit is its second since Trump took office.
The Tigers last visited in June 2017 after their championship run the previous season. That day, the White House served a barbecue lunch that star wide receiver Hunter Renfrow called at the time "the best meal I've had in a year."
Clemson coach Dabo Swinney has nominated this season's undefeated Tigers as the best college team ever. Trump called them a "great team, an unbelievable team."
The president lauded the Tigers for their 44-16 win over Alabama last week, singling out Renfrow, cornerback A.J. Terrell and defensive coordinator Brent Venables.
He saved his highest praise for Clemson quarterback Trevor Lawrence,
"Oh I want to be the agent for that tall, handsome quarterback," Trump said. "Six foot seven, they say great athlete, and he's accurate. That's nice."
Before going to the White House, coaches and players toured some landmarks in Washington, including the Lincoln Memorial.
"What a fun day it's been," Swinney said."It's an honor to be a part of this tradition, and to be honest with you, it's really cool that football can create an opportunity like this."
The Associated Press contributed to this report.