Even if this works fine in JS, as Stylesheet.create simply returns the object passed as a parameter, it throws a typing error in TS. The method is typed as followed:

export namespace StyleSheet {
  type NamedStyles<T> = {[P in keyof T]: ViewStyle | TextStyle | ImageStyle};

  /**
   * Creates a StyleSheet style reference from the given object.
   */
  export function create<T extends NamedStyles<T> | NamedStyles<any>>(
    styles: T | NamedStyles<T>,
  ): T;
}

Here you can see that it takes an object as a parameter where each value must be of type ViewStyle | TextStyle | ImageStyle.
As mentioned by @DanielGabor you can still create a style object without using Stylesheet.create where keys return functions that themselves return ViewStyle | TextStyle | ImageStyle

See this answer:

https://stackoverflow.com/a/37144690/3850405

If you only need css for a class in your component you could do it like below. I like this solution for when inline css does not work and only small changes are needed.

import * as React from "react";
import { Header } from "./header";

export class Home extends React.Component<{}, {}> {
    render() {
        const css = `
        .landing-page {
            background-color: orange;
        }
        `
        return (
            <div>
                <style>
                    {css}
                </style>
                <div id="page-top" className="landing-page">
                    <Header />
                </div>
            </div>  
        );
    }
}

A) As you are saying, there is one simplest (not best) option to use require:

const css = require('./component.css')

• We need to have typings for require as it's not standard feature in typescript.

• Simplest typing for this specific require may be:

  declare function require(name: string): string;
  

• Webpack will then compile typescript and use modules properly - BUT without any IDE help and class names checks for build.

B) There is better solution to use standard import:

import * as css from './component.css'

• enables full class names IntelliSense
• requires types definition for each css file, otherwise tsc compiler will fail

For proper IntelliSense, Webpack needs to generate types definition for each css file:

1. Use webpack typings-for-css-modules-loader

   webpackConfig.module.loaders: [
     { test: /\.css$/, loader: 'typings-for-css-modules?modules' }
     { test: /\.scss$/, loader: 'typings-for-css-modules?modules&sass' }
   ];
   

2. Loader will generate *.css.d.ts files for each of css files in your codebase

3. Typescript compiler will understand that css import will be module with properties (class names) of type string.

Mentioned typings-for-css-loader contains a bug and because of types file generation delay, it's best to declare global *.css type in case our *.css.d.ts file is not generated yet.

That little bug scenario:

1. Create css file component.css
2. Include it in component import * as css from './component.css'
3. Run webpack
4. Typescript compiler will try to compile code (ERROR)
5. Loader will generate Css modules typings file (component.css.d.ts), but it's late for typescript compiler to find new typings file
6. Run webpack again will fix build error.

Easy fix is to create global definition (eg. file called typings.d.ts in your source root) for importing CSS Modules:

declare module '*.css' {
  interface IClassNames {
    [className: string]: string
  }
  const classNames: IClassNames;
  export = classNames;
}

This definition will be used if there is no css file generated (eg. you have added new css file). Otherwise will be used generated specific (needs to be in same folder and named same as source file + .d.ts extension), eg. component.css.d.ts definition and IntelliSense will work perfectly.

Example of component.css.d.ts:

export const wrapper: string;
export const button: string;
export const link: string;

And if you don't want to see generated css typings you may setup filter in IDE to hide all files with extension .css.d.ts in your sources.