Showunmi, 26, turned down a move to Leeds in January even though a transfer fee had been agreed and talks with former manager Dennis Wise had reached an advanced stage.
A week later, Showunmi joined Sheffield Wednesday on loan, but returned to Ashton Gate two months later without a goal in 10 appearances in South Yorkshire.
"I'm raring to go and I'm looking forward to pre-season and playing games," he said. "I'm delighted to be here. You only have to look at this club with its history and its fanbase to see how big it is."
Showunmi made 61 appearances for Bristol City and scored 18 times during a two-season spell which included an automatic promotion from League One.