A rep for the House actress confirmed to the news to People earlier today.
The 28-year-old Tamblyn has starred in a number of films, such as The Sisterhood of the Travelling Pants and 127 Hours. However, she is most famous for her television work, having played the lead in the series Joan of Arcadia from 2003 to 2006.
Meanwhile, Cross portrayed Tobias Fünke on the popular sitcom Arrested Development. He currently stars on the British-American comedy TV series The Increasingly Poor Decisions of Todd Margaret.
The couple, who have been dating since 2009, are said to have been engaged for a while.
"They've been engaged for weeks," a source told Life & Style.
Tamblyn previously confessed that leaving House was difficult, revealing that she was in tears when she discovered House star Hugh Laurie had thrown her a surprise party for her departure.
An Arrested Development movie that would see Cross return to the role of Tobias is said to be in the works.