Dedicating a home in Israel is a mitzva. This becomes clear in the following verse, which addresses the question of who goes out to fight in wartime and who is sent home: “Is there anyone who has built a new house but has not dedicated it (chanacho)? Let him go back to his home” (Devarim 20:5). Commentators explain that the verse is referring to a home that there is a mitzva to dedicate, and this must be in a place where there is a mitzva to live, namely the Land of Israel.
Dedicating something (chinuch) is usually associated with a beginning. So, when the verse says that the person “has not dedicated it,” this means he has not started living there. More specifically, according to Targum Yonatan, it means he has not yet put up a mezuzah, while the Radak says that it means he has not yet had a meal there.
Some believe that a meal served at a home dedication or house-warming is not considered a seudat mitzva unless there are divrei Torah (words of Torah). Others maintain that in Israel, the meal of a home dedication is automatically a seudat mitzva, even without accompanying divrei Torah. It is only in the Diaspora that divrei Torah are required in order to transform the meal into a seudat mitzva.
Since buying a new item of clothing requires reciting the blessing of Shehecheyanu, it would certainly seem that buying a new home should require it as well. However, Shehecheyanu is recited only when the person is the only beneficiary of the new item. In general, a person buys a home for himself and his family. Therefore, Shehechiyanu is not recited.