The acquisition has been made through the Whittalls Wine Merchants subsidiary of EFB's retail division and includes the "trade and assets" of the stores.
EFB said the move had saved more than 200 jobs and would see the company move into Scotland and London for the first time.
EFB became a significant player in the off-licence business with the acquisition of a package of 109 Wine Cellar stores trading as Simply Drinks and Booze Buster in 2009.
Raj Chatha, EFB's owner, said: "We are pleased to welcome Oddbins colleagues to the EFB Group and team.
"The addition to our retail estate means we can truly call ourselves a national player.
"This represents a new dawn for these Oddbins stores, and with the well-reported financial shackles removed, it will allow for a consistent supply of stock and investment at store level for the benefit of all, most importantly its loyal staff and consumer base.
“Our focus over the coming weeks and months will be to replenish the stores with an exciting range at competitive prices. I am also delighted with the number of jobs we have managed to save.”