This example will work if you compile ES6 modules syntax into ES5, because in the end, all module exports belong to the same object, which can be modified.

import { allowThrough } from './allowThrough';
import { ENABLED } from './constants';
import * as constants from './constants';

describe('allowThrough', () => {
    test('success', () => {
        constants.ENABLED = true;

        expect(ENABLED).toBe(true);
        expect(allowThrough({ value: 1 })).toBe(true);
    });

    test('fail, ENABLED === false', () => {
        constants.ENABLED = false;

        expect(ENABLED).toBe(false);
        expect(allowThrough({ value: 1 })).toBe(false);
    });
});

Alternatively, you can switch to raw commonjs require function, and do it like this with the help of jest.mock(...):

const mockTrue = { ENABLED: true };
const mockFalse = { ENABLED: false };

describe('allowThrough', () => {
    beforeEach(() => {
        jest.resetModules();
    });

    test('success', () => {
        jest.mock('./constants', () => mockTrue)
        const { ENABLED } = require('./constants');
        const { allowThrough } = require('./allowThrough');

        expect(ENABLED).toBe(true);
        expect(allowThrough({ value: 1 })).toBe(true);
    });

    test('fail, ENABLED === false', () => {
        jest.mock('./constants', () => mockFalse)
        const { ENABLED } = require('./constants');
        const { allowThrough } = require('./allowThrough');

        expect(ENABLED).toBe(false);
        expect(allowThrough({ value: 1 })).toBe(false);
    });
});

There is another way to do it in ES6+ and jest 22.1.0+ thanks to getters and spyOn.

By default, you cannot spy on primitive types like boolean or number. You can though replace an imported file with your own mock. A getter method still acts like a primitive member but allows us to spy on it. Having a spy on our target member you can basically do with it whatever you want, just like with a jest.fn() mock.

Below an example

// foo.js
export const foo = true; // could be expression as well

// subject.js
import { foo } from './foo'

export default () => foo

// subject.spec.js
import subject from './subject'

jest.mock('./foo', () => ({
  get foo () {
    return true // set some default value
  }
}))

describe('subject', () => {
  const mySpy = jest.spyOn(subject.default, 'foo', 'get')

  it('foo returns true', () => {
    expect(subject.foo).toBe(true)
  })

  it('foo returns false', () => {
    mySpy.mockReturnValueOnce(false)
    expect(subject.foo).toBe(false)
  })
})

Read more in the docs.

Unfortunately none of the posted solutions worked for me or to be more precise some did work but threw linting, TypeScript or compilation errors, so I will post my solution that both works for me and is compliant with current coding standards:

// constants.ts
// configuration file with defined constant(s)
export const someConstantValue = true;

// module.ts
// this module uses the defined constants
import { someConstantValue } from './constants';

export const someCheck = () => someConstantValue ? 'true' : 'false';

// module.test.ts
// this is the test file for module.ts
import { someCheck } from './module';

// Jest specifies that the variable must start with `mock`
const mockSomeConstantValueGetter = jest.fn();
jest.mock('./constants', () => ({
  get someConstantValue() {
    return mockSomeConstantValueGetter();
  },
}));

describe('someCheck', () => {
  it('returns "true" if someConstantValue is true', () => {
    mockSomeConstantValueGetter.mockReturnValue(true);
    expect(someCheck()).toEqual('true');
  });

  it('returns "false" if someConstantValue is false', () => {
    mockSomeConstantValueGetter.mockReturnValue(false);
    expect(someCheck()).toEqual('false');
  });
});