Where is the syntax for TypeScript comments documented?

Current

The TypeScript team, and other TypeScript involved teams, created a TSDoc specification. https://tsdoc.org/

Example straight from the docs:

export class Statistics {
  /**
   * Returns the average of two numbers.
   *
   * @remarks
   * This method is part of the {@link core-library#Statistics | Statistics subsystem}.
   *
   * @param x - The first input number
   * @param y - The second input number
   * @returns The arithmetic mean of `x` and `y`
   *
   * @beta
   */
  public static getAverage(x: number, y: number): number {
    return (x + y) / 2.0;
  }
}

Past

TypeScript uses JSDoc. e.g.

/** This is a description of the foo function. */
function foo() {
}

To learn jsdoc : https://jsdoc.app/

But you don't need to use the type annotation extensions in JSDoc.

You can (and should) still use other jsdoc block tags like @returns etc.

Just an example. Focus on the types (not the content).

JSDoc version (notice types in docs):

/**
 * Returns the sum of a and b
 * @param {number} a
 * @param {number} b
 * @returns {number}
 */
function sum(a, b) {
    return a + b;
}

TypeScript version (notice the re-location of types):

/**
 * Takes two numbers and returns their sum
 * @param a first input to sum
 * @param b second input to sum
 * @returns sum of a and b
 */
function sum(a: number, b: number): number {
    return a + b;
}

Update November 2020

A website is now online with all the TSDoc syntax available (and that's awesome): https://tsdoc.org/

---

For reference, old answer:

The right syntax is now the one used by TSDoc. It will allow you to have your comments understood by Visual Studio Code or other documentation tools.

A good overview of the syntax is available here and especially here. The precise spec should be "soon" written up.

Another file worth checking out is this one where you will see useful standard tags.

Note: you should not use JSDoc, as explained on TSDoc main page: Why can't JSDoc be the standard? Unfortunately, the JSDoc grammar is not rigorously specified but rather inferred from the behavior of a particular implementation. The majority of the standard JSDoc tags are preoccupied with providing type annotations for plain JavaScript, which is an irrelevant concern for a strongly-typed language such as TypeScript. TSDoc addresses these limitations while also tackling a more sophisticated set of goals.