Adam Purinton, 51, fled the scene of the attack at a pub in Olathe and went to a restaurant where he confided in a staff member, police say.
He was arraigned in court on Monday with first-degree murder and two counts of attempted first-degree murder.
The accused wore a safety smock to prevent him from harming himself.
He allegedly fired on Mr Kuchibhotla and his friend Alok Madasani, two 32-year-old Indian men who worked as engineers at GPS-maker Garmin.
Mr Kuchibhotla died and Mr Madasani survived. A third patron, 24-year-old Ian Grillot, was wounded trying to intervene.
The FBI is investigating whether the shooting constitutes a hate crime.
After the attack at Austins Bar and Grill, the suspect, who is white, drove 70 miles (112km) to an Applebee’s in Clinton, Missouri, where he allegedly admitted what he had done to an employee.
On Saturday at 11am, the doors of Austin Bar and Grill reopened, after a fatal shooting which has shaken people here in Olathe and beyond.
“We’ve come back to show we won’t let the attacker change our way of life,” said one patron who’d turned up.