The 27-year-old last month comfortably outpointed Arthur Abraham, and has joined fellow Britons George Groves, Jamie Cox and Callum Smith in the super-middleweight edition of the eight-fighter competition.
Eubank Jr has been installed as the 1/5 favourite to win the fight by Sky Bet, with Yildirim 100/30 and the draw 33/1.
October's quarter-final fixture also represents only Eubank Jnr's second fight overseas, having won in Denmark in his sixth as a professional, and he said: "I don't mind about fighting in Germany. I honestly don't mind where I fight.
"I could be fighting in a phone box. It really doesn't matter to me as long as I get the win that's all I care about.
"The Muhammad Ali Trophy is a great idea and I am thrilled to be a part of the World Boxing Super Series.
"Yildirim's chin hasn't been tested, I will test it to the absolute limit and if it has even the slightest bit of weakness he won't last six rounds."
Turkey's undefeated Yildirim, 26, in 2015 outpointed respected former world champion Glen Johnson, and criticised Eubank Jnr's presence at Floyd Mayweather's camp in the build-up to the American's fight with Conor McGregor.
Bet now on Chris Eubank v Avni Yildirim!
"What is Chris going to learn there, apart from hide-and-seek?," he said. "I like Mayweather, he is a special guy. But Eubank is not Mayweather. Seriously, what is he going to learn from a welterweight, to run away for 12 rounds?
"The fans want a fight, I want a fight. If he is man enough, me versus Chris will be a good fight."
Smith fights Erik Skoglund at the Liverpool Arena on September 16, while WBA champion Groves makes the first defence of his title against Cox at Wembley's SSE Arena a week after Eubank-Yildirim.
The fourth quarter-final is between Germany's Juergen Braehmer and Rob Brant; a date and venue are still to be finalised.
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