The offer of $12.25 per share is at a premium of 49 percent to Zipcar's Monday close.
"We see car sharing as highly complementary to traditional car rental, with rapid growth potential and representing a scalable opportunity for us as a combined company," Ronald Nelson, Avis' chief executive, said in a statement.
Rising gasoline prices have driven demand for car sharing, attracting car rental companies. Enterprise Holdings, the largest U.S. car rental company, is also expanding aggressively in the car-sharing market.
However, Zipcar has struggled to grow its presence in smaller cities to counter the threat of a saturating market in bigger cities. It is also encountering increased competition from traditional car rental companies such as Hertz Global Holdings and Enterprise.
The deal, expected to close in the spring of 2013, will add to Avis' earnings, excluding items, from the second year and is expected to generate between $50 million and $70 million in annual synergies.
Avis said it expects to fund the transaction primarily with available cash and additional debt. The company had cash and marketable securities of about $554 million as of Sept. 30.
Zipcar's shares closed at $8.24 on the Nasdaq on Monday. Avis' shares closed at $19.82.