To use these libraries from Typescript, you can either create so-called ambient definitions for the JS library manually, or use existing Typescript definition files (extension .d.ts).
The TypeScript source code repository contains a jquery.d.ts in the /bin directory, and a definition file for jquery.ui can be found in /samples/warship. However, those samples need not cover the respective library completely.
The project aims to provide high quality definitions for the most popular libraries out there.
which lists about 50 definition files covering major JS libraries and frameworks.