Keith Mitchell's New National Party defeated the National Democratic Congress of outgoing leader Tillman Thomas in Tuesday's vote. Thomas had served as prime minister since 2008.
Elections supervisor Judy Benoit says preliminary results show the NNP received more than 31,000 votes and the NDC more than 20,000.
Grenada has nearly 110,000 inhabitants.
The 13 seats in the island's Senate are indirectly determined by the election. The new government appoints 10 of the seats while the opposition names three.