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"They are really thrilled," says the rep.
The couple, who met on the set of ABC's Men In Trees, began dating in 2007.
Tupper, 43, told PEOPLE at the time he was "not ready to rush into marriage [but] never met anyone like her. There's something really comforting when you can truly connect with someone and be understood."
Heche, 39, has a 6-year-old son, Homer, from her marriage to Coley Laffoon. The two separated in early 2007 and reached a divorce settlement in June.
• Visit the Celebrity Baby Blog to leave your well-wishes for the Men in Trees star
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