Sharepoint - SPFx - How to call function on button click event from ts file with React

Add a property to your IAutoCompleteProps interface for your click handler. Then pass the function from the AutoCompleteWebPart into the interface as one of the component's properties.

So in your IAutoCompleteProps something like this:

export interface IAutoCompleteProps {
  //Other properties
  clickHandler: () => void;
}

Then in your AutoCompleteWebPart render:

public render(): void {
    const element: React.ReactElement<IAutoCompleteProps > = React.createElement(
      AutoComplete,
      {
        //Other props
        clickHandler: this.button_click
      }
    );

    ReactDom.render(element, this.domElement);
}

Then in your AutoComplete component JSX portion:

<button onClick={this.props.clickHandler}>CLICK ME</button>