Swashbuckle - swagger documentation of returned response?

You can specify the response type with the following attribute:

[ProducesResponseType(typeof(UserCreateResponse), 200)]

The below solution works only for Swashbuckle versions prior to V6.0!

From V6.0 onwards SwaggerResponse isn't supported anymore, see here.

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Another variant is the use of the SwaggerResponse attribute, which also allows to provide an additional description:

[SwaggerResponse(HttpStatusCode.OK, "UserDTO", typeof(UserDTO))]
public async Task<IHttpActionResult> Get([FromODataUri] int key)
{
    var result = await UserRepo.GetAsync(key);
    ...
    return Ok(result);
}

which produces output as shown here:

It's also possible to omit the type to document other status codes which do not return an entity:

[SwaggerResponse(HttpStatusCode.NotFound, "no data found")]
[SwaggerResponse(HttpStatusCode.BadRequest, "requiered request headers not found")]

Starting from .NET Core 2.1, using ActionResult<T> would be the recommended approach to specify the returned type. It gets picked by Swashbuckle and also adds type checks at the compilation.

You also can add description on the response via XML comment (docs).

So for the OP's example it would be

/// <summary> 
///     Update the user 
/// </summary>
/// <response code="200"> User's data </response>
[HttpPost]
[ProducesResponseType(StatusCodes.Status200OK)]
public async Task<ActionResult<UserCreateResponse>> Update(...) 
{
   ...
}