Version of used dependencies:

$ node --version
v10.16.0
$ npm --version
6.9.0
$ npx tsc --version
Version 3.5.3
$ npx jest --version
24.9.0

Jest configuration file jest.config.js for typescript:

module.exports = {
  preset: "ts-jest",
  testEnvironment: "node",
  testRegex: "/__tests__/(.*).spec.ts$",
};

VScode run configuration launch.json to run typescript test using jest:

{
    "version": "0.2.0",
    "configurations": [
        {
            "name": "Debug Jest Tests",
            "type": "node",
            "request": "launch",
            "args": [
                "--inspect-brk",
                "${workspaceRoot}/node_modules/.bin/jest",
                "--runInBand",
                "--config",
                "${workspaceRoot}/jest.config.js"
            ],
            "console": "integratedTerminal",
            "internalConsoleOptions": "neverOpen"
        }
    ]
}