You can re-assign global.expect 's runtime value on javascript side, on the typescript side however, no easy way out.
Jest declares expect as a global variable (see @types/jest/index.d.ts(39, 15) ). Currently typescript provides no way to override a readily declared variable's type in the same block-scope.
So as long as you keep @types/jest/index.d.ts the way it is, nothing you can do to suppress that error.

Solution

1. The easy way

The easiest way to use chai's expect , is simply import and use it in every .test.ts file:

// sum.test.ts
import { expect } from 'chai'
import { sum } from './sum';

test('adds 1 + 2 to equal 3', () => {
  expect(sum(1, 2)).eq(3)
});

2. The hard way

Now if you really can't live with that repeating import { expect } from 'chai' line, here's the harder path:

1. Move node_modules/@types/jest to types/jest , make sure it's gone in the node_modules folder. Also delete "@types/jest" from "package.json => devDependencies".
2. Modify types/jest/index.d.ts , replace the type of expect with chai's. You need to commit this customized type declaration to your git repo.

// index.d.ts

+ /// <reference types="chai" />

- declare const expect: Expect
+ declare const expect: Chai.ExpectStatic

1. In your tsconfig.json , add:

{
  "compilerOptions": {
    "typeRoots": ["node_modules/@types", "types"],
    ...
}

1. Create jestSetup.js and add this one-liner:

global.expect = require("chai").expect

1. in jest.config.js , set:

setupFilesAfterEnv: ['./jestSetup.js'],
// or `setupTestFrameworkScriptFile` for older version.

There you go. You can now use chai expect right in the global scope.