When dedicating a new home, the shehecheyanu blessing is recited.

The words are:

Baruch Ata A-do-nai Elo-heinu Melech Haolam she-hech-e-ya-nu v'ki-ma-nu v'hi-gi-ya-nu li-z'man hazeh.

Blessed are You, L-rd our G‑d, King of the Universe, who has granted us life, sustained us and enabled us to reach this occasion.

This blessing is recited on certain joyous occasions, such as when doing a mitzvah which does not happen on a regular basis (example: when lighting the menorah on the first night of Chanukah), on Biblical holidays, when purchasing a valuable article of clothing, or when eating a new fruit for the first time in its season.

Similarly, on the occasion of buying a new home — which certainly is a joyous occasion — this blessing is recited.

For various reasons,1 the custom today is that when celebrating the housewarming, a new fruit is eaten, and the shehecheyanu blessing is recited while having in mind that it should apply to both the new home and the new fruit.

May you always write with good news,

Rabbi Baruch S. Davidson

P.S. Upon entering a new home, one is required to affix a mezuzah to its doorways. A blessing is recited when doing this special mitzvah:2

Bah-rookh ah-tah ah-doh-noi eh-loh-hay-noo meh-lekh hah-oh-lahm ah-sher ki-deh-shah-noo beh-mitz-voh-tahv veh-tzee-vah-noo lik-boh-ah meh-zoo-zah.

Blessed are You, L-rd our G‑d, King of the universe, who has sanctified us with His commandments and commanded us to affix a mezuzah

Refer to the following links for more information on these topics:

Moving in to a new home
The shecheyanu blessing
Mezuzah