* Idemitsu's founding family drops opposition to merger
* Idemitsu shares jump 15 pct, Showa Shell up 9 pct (Adds background, detail, share prices)
TOKYO, July 10 (Reuters) - Japanese oil refiners Idemitsu Kosan and Showa Shell Sekiyu said on Tuesday they had agreed to merge in April next year, after Idemitsu's founding family dropped its long-standing opposition to the plan.
The refiners will merge via a share swap, and Showa Shell will be delisted, they said in a statement, pushing the shares of the two companies up sharply in morning trade.
Idemitsu, Japan's No.2 oil refiner by sales, has long been keen to merge its operations with fourth-ranked Showa Shell in response to shrinking gasoline demand in the country.
But it was locked in a battle for about two years with the Idemitsu founding family, which argued the two firms were too different for any merger to work.
As part of the deal announced on Tuesday, the founding family will be able to nominate two of the eight initial directors of the merged entity.
The share swap ratio will be set in October, the companies said.
In addition, Idemitsu said it would buy back up to 55 billion yen ($495 million) of its own shares through December to return profits to current shareholders before the merger.
Shares of Idemitsu surged 15 percent and Showa Shell jumped 9 percent by the midday break on the Tokyo Stock Exchange. ($1 = 111.0200 yen) (Reporting by Osamu Tsukimori; Writing and additional reporting by Chris Gallagher; editing by Richard Pullin)