As of TypeScript 1.8, it is possible to combine JavaScript and TypeScript in the same project. Thus, you can migrate a project file by file.
During the migration of the files, the project should be working at every step. That way, you can check that the work is going well, and you can still work on the project. If an urgent bug is reported, you do not have to fix it in the old and migrated version; you only have to fix it in the current version.
You can convert the project in the following steps:
Add the TypeScript compiler to the project
Migrate each file
Refactor and enable stricter checks of TypeScript
In the next sections, we will see how these steps can be done.