How to define global function in TypeScript?

You're defining the type for the compiler, but not actually attaching it to the global namespace — window in the browser, global in node. Instead of exporting it from the module, attach it. For isomorphic use, use something like...

function s() { ... }

// must cast as any to set property on window
const _global = (window /* browser */ || global /* node */) as any
_global.s = s

You can also ditch the .d.ts file and declare the type in the same file using declare global, e.g.

// we must force tsc to interpret this file as a module, resolves
// "Augmentations for the global scope can only be directly nested in external modules or ambient module declarations."
// error
export {}

declare global {
  function s<T>(someObject: T | null | undefined, defaultValue?: T | null | undefined) : T;
}

const _global = (window /* browser */ || global /* node */) as any
_global.s = function<T>(object: T | null | undefined, defaultValue: T | null = null) : T {
  if (typeof object === 'undefined' || object === null)
    return defaultValue as T;
  else
    return object;
}

global.ts(x) needs just a little tweak to be a valid "global module" (a module with side effects only): remove the export keyword and add some code to augment the global object. You can also provide the global declaration in the same file and remove global.d.ts.

function _s<T>(object: T | null, defaultValue: T = {} as T) : T {
    return object == null
        ? defaultValue
        : object as T;
}

// Global declaration
declare var s: typeof _s;

// Global scope augmentation
var window = window || null;
const _global = (window || global) as any;
_global.s = _s;

To use it, just import the module once, for instance in App.tsx via a global import: import './global';.

Tested with mocha, chai, ts-node:

import { expect } from 'chai';
import './global'; // To do once at app bootstrapping

describe('global s()', () => {
    it('should replace null with empty object', () => {
        const result = s(null);
        expect(result).to.eql({});
    });

    it('should replace undefined with empty object', () => {
        const result = s(undefined);
        expect(result).to.eql({});
    });

    it('should replace null with the given default value', () => {
        const defVal = { def: 'val' };
        const result = s(null, defVal);
        expect(result).to.eql({ def: 'val' });
    });

    it('should preserve defined object', () => {
        const object = { bar: 'a' };
        const result = s(object);
        expect(result).to.eql(object);
    });
});

Thanks to @Romain Deneau. His answer worked for me. Here is my simplified one to make it look easier to get the point of his answer. (Mine assumes the scripts run on a browser. Also, I omitted signature of function s.)

Define function outside of any class.

function s() {
    console.log("invoked s()!");
}

(window as any).s = s;

Using this global function s from TypeScript class is like below;

declare var s;

export class MyClass {
    public static callFunctionS() {
        s();
    }
}