Delton, a fifth-year graduate transfer, started the Horned Frogs' first two games, but was replaced by true freshman Max Duggan.
Delton completed 27 of 50 attempts this season for 318 yards, no touchdowns and one interception.
His departure follows that of redshirt freshman Justin Rogers, who announced last week he plans to transfer.
Delton told the Fort Worth Star-Telegram that he has "nothing but great things to say" about the program and its future.
"Coach P is a phenomenal, top-notch head coach at a first-class program. Coach handles business the right way," Delton told the newspaper. "Nothing but love and gratitude toward TCU and the people of Fort Worth."
TCU's quarterback depth is in question for its upcoming game against No. 11 Baylor.
"I think Max will play," Patterson said.
Duggan has started six games, including a win over then-No. 15 Texas. He has completed 120 passes on 208 attempts for 1,405 yards with 12 touchdowns and four interceptions for the Horned Frogs (4-4, 2-3 Big 12).