Having error “Module ‘name’ resolves to an untyped module at…” when writing custom TypeScript definition file

The actual solution is given in a comment by @Paleo in @hirikarate’s answer:

Imports should be declared inside the module declaration.

Example:

declare module 'node-helper-lib' {
   import * as SomeThirdParty from 'node-helper-lib';
   interface Helper {
       new(opt: SomeThirdParty.Options): SomeThirdParty.Type
   }
   export = Helper;
}