Gunners land Braga and Partizan Belgrade in Group H...
The Croatian striker left the Gunners for the Ukrainian side this summer after three years in London, completing a £7 million transfer last month.
However, the Brazilian-born star retains a special place in the hearts of Gunners fans following his fight back from a career-threatening leg injury sustained against Birmingham City in 2008.
"The draw always throws up something good," Gazidis told Sky Sports. "I think it's great we are going to see Eduardo back at the Emirates stadium and I know he'll get a very warm welcome there with Shakhtar Donetsk."
Gazidis believes the Gunners will be tested not only by second seeds Shakhtar but by other group rivals Braga and Partizan Belgrade.
Referring to Braga's route through qualification, Gazidis said: "Anyone that can beat Celtic and Sevilla on their way to the group phase is a good team so we'll be ready for them as well."
On the possibility of playing in the final of the competition which is being held at Wembley next May, Gazidis added: "There's a real incentive for the London club.
"It would be fantastic to play in the final in London so there's a mini competition there."