Microsoft Corp. has agreed to acquire 6Wunderkinder GmbH, a Berlin-based startup behind the Wunderlist to-do list app, for between $100 million and $200 million, according to a person familiar with the deal.

The purchase is part of Microsoft’s new effort to enhance its line of mobile apps. It has recently started offering the mobile version of Microsoft Office free and acquired two makers of mobile apps: San Francisco-based Acompli Inc., which makes mobile-email applications, and Sunrise Atelier Inc., a New York-based startup...