The 32-year-old defender was released by Ahli last month, and moved to Ittihad on a one-year deal after turning down several bids from abroad.
During the conference, Ittihad chairman Mohamed Moselhi expressed his delight at the signing completion.
"It's been a while since we completed such a big signing," he said.
Petroleum Sector
Moselhi pointed out that it's hard for Ittihad to land high-profile players these days, thanks to the free-spending policy of the petroleum sector clubs.
"I have nothing against the petroleum sector clubs (Petrojet, ENPPI and Asyut Petroleum)," he explained.
"All I'm saying is that they receive huge financial support, and that's why they can purchase any player they want.
"But eventually we managed to secure a big signing."
From his side, Shadi said: "Ittihad are a great club and I really like their fans. I think they deserve to win a title, and I hope I can help them claim one."
Different
The conference also witnessed the announcement of Taha Basri's contract extension for one more year.
The Ittihad boss insinuated that the Alexandrian side would be in contention for the league title next season.
"This season is going to be totally different for us than all previous seasons. We bolstered the squad with competent newcomers and kept hold of the key figures," he stated.
Before signing Shadi, Ittihad brought in several players, including Mohamed Al-Morsi and Osama Hassan from Zamalek, after both men fell down the pecking order at the Cairo club.
The newly-signed duo also attended the news conference.
Ittihad are expected to wrap up more deals in the near future.