Quite old question, but this was my fix as of 2025:

npm install -D tsx

in package.json:

{
    "scripts": {
        "test-old": "mocha -r ts-node/register tests/**/*.test.ts",
        "test": "mocha -r tsx tests/**/*.test.ts",
    }
}

ts-node/register did not work, but tsx saved the day. Thanks to Jazcash