The 56-year-old German was unveiled at a press conference by Iraqi Football Association (IFA) president Hussein Saeed in the northern Iraqi city of Arbil on Monday, the Asian Football Confederation website reported on Tuesday.
"My mission with the Iraqi team will not be easy because I will be the manager during the Asian Cup," Sidka was quoted as saying. "I will be sure to put together a strong side."
Sidka, who was Werder coach in the late 1990s, already has experience of coaching in Asia through stints in charge of Bahrain and two Qatari club sides.
Iraq's Asian title defence had looked in jeopardy earlier this month when they were on the brink of suspension from international soccer because of a political power struggle that has paralysed the IFA.
Two attempts to elect a new president in Arbil last month failed because too few delegates made the journey to the city in Iraqi Kurdistan, where FIFA had decided the vote should take place for security reasons.
FIFA, however, last week gave the IFA one year to settle the row, which highlighted sectarian divisions in the country seven years after the U.S.-led invasion.
Iraq has been grouped with Iran, the United Arab Emirates and North Korea for next year's Asian Cup, which takes place from January 7-29.
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
'People around the world know me because of my goal at Chelsea. I still can’t explain it, though. Drogba even asked me, 'Who are you? What did you eat?"' Newcastle cult hero Papiss Cisse recalls iconic strike at Stamford Bridge
